# The Mereon Matrix

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## The Mereon Matrix

Author | : Lynnclaire Dennis,Jytte Brender McNair,Louis H. Kauffman |

Publsiher | : Newnes |

Total Pages | : 602 |

Release | : 2013-05-21 |

ISBN 10 | : 0124046886 |

ISBN 13 | : 9780124046887 |

Language | : EN, FR, DE, ES & NL |

**The Mereon Matrix Book Review:**

Mereon is an approach to the unification of knowledge that relies on whole systems modelling. It is a scientific framework that charts the sequential, emergent growth process of systems. A dynamic structure, Mereon provides insight and a new approach to General Systems Theory and non-linear science. Mereon evolved through a new approach to polyhedral geometry and topology that is related to the dynamics of the polyhedra. It is related to a large number of systems, physical, mathematical, and philosophical. In linking these systems, Mereon provides access to new relationships among them and combines geometric and process thinking. This book provides the fundamentals of such connections for an ongoing search for order, directionality, and diversity that is found in this unity. It is written in clear language that manages to connect diverse disciplines and in doing so, makes a complex system easily accessible and understandable. It will be of interest to mathematicians, geneticists, and all those interested in researching unity in science and astrobiology. Elaborates on several important aspects of General Systems Theory including nonlinearity. Each chapter is self-contained and explained relative to Mereon, providing references to scientific findings that are congruent with or expanded by Mereon. Offers a new way of modelling that can be applied across the sciences.

## The Mereon Matrix

Author | : Jytte Brender McNair,Lynnclaire Dennis,Louis H. Kauffman |

Publsiher | : World Scientific Publishing Company |

Total Pages | : 950 |

Release | : 2018 |

ISBN 10 | : 9789813233553 |

ISBN 13 | : 9813233559 |

Language | : EN, FR, DE, ES & NL |

**The Mereon Matrix Book Review:**

## Mereon Matrix The Everything Connected Through K nothing

Author | : Kauffman Louis H,Mcnair Jytte Brender,Dennis Lynnclaire |

Publsiher | : World Scientific |

Total Pages | : 904 |

Release | : 2018-06-12 |

ISBN 10 | : 9813233575 |

ISBN 13 | : 9789813233577 |

Language | : EN, FR, DE, ES & NL |

**Mereon Matrix The Everything Connected Through K nothing Book Review:**

In this richly illustrated book, the contributors describe the Mereon Matrix, its dynamic geometry and topology. Through the definition of eleven First Principles, it offers a new perspective on dynamic, whole and sustainable systems that may serve as a template information model. This template has been applied to a set of knowledge domains for verification purposes: pre-life-evolution, human molecular genetics and biological evolution, as well as one social application on classroom management. The importance of the book comes in the following ways: The dynamics of the geometry unites all Platonic and Kepler Solids into one united structure and creates 11 unique trefoil knots. Its topology is directly related to the dynamics of the polyhedra. The Mereon Matrix is an approach to the unification of knowledge that relies on whole systems modelling. it is a framework charting the emergence of the Platonic and Kepler solids in a sequential, emergent growth process that describes a non-linear whole system, and includes a process of 'breathing' as well as multiplying ('birthing'); This dynamic/kinematic structure provides insight and a new approach to General Systems Theory and non-linear science, evolving through a new approach to polyhedral geometry. A set of 11 First Principles is derived from the structure, topology and dynamics of the Mereon Matrix, which serve well as a template information model. The Mereon Matrix is related to a large number of systems, physical, mathematical, and philosophical, and in linking these systems, provides access to new relationships among them by combining geometry with process thinking. The new perspective on systems is hypothesized as universal -- this is, applicable in all areas of science, natural and social. Such applicability has been demonstrated for applications as diverse as pre-life evolution, biological evolution and human molecular genetics, as well as a classroom management system for the educational system. Care has been taken to use images and languaging that are understandable across domains, connecting diverse disciplines, while making this complex system easily accessible. Contents: Prologues: Sustainability: Mathematical Elegance, Solid Science and Social Grace (L Dennis and L H Kauffman) Lynnclaire Dennis & R Buckminster Fuller Investigation (R W Gray) The Matrix We Call Mereon (L H Kauffman) First Things First: Building on the Known: A Quintessential Jitterbug (L Dennis, J Brender McNair, N J Woolf and L H Kauffman) Methodology (J Brender McNair and L Dennis) Philosophical Thoughts and Thinking Aloud Allowed (L Dennis) Belonging -- Education as Transformation (L Dennis) Meme, Pattern and Perspective (L Dennis, N J Woolf and L H Kauffman) Including and Beyond the Point: The Context -- Form Informing Function (L Dennis, J Brender McNair, N J Woolf and L H Kauffman) Flow and Scale (L Dennis and L H Kauffman) The Core -- Sharp Distinctions to Elegant Curves (L Dennis and L H Kauffman) Connections, Ligatures and Knots: Mereon Thoughts -- Knots and Beyond (L H Kauffman) The Mereon Trefoil -- Asymmetrical with Perfect Symmetry (L Dennis) Applying Mereon to Knowledge Domains: Exploring the Mereon Matrix (and Beyond) with the CymaScope Technology (L Dennis and P McNair) The Origin of Matter: Life, Learning and Survival (N J Woolf and L Dennis) ATCG -- An Applied Theory for Human MoleCular Genetics (J Brender McNair, P McNair,

## Handbook of Evaluation Methods for Health Informatics

Author | : Jytte Brender McNair |

Publsiher | : Elsevier |

Total Pages | : 368 |

Release | : 2006-01-17 |

ISBN 10 | : 0080533450 |

ISBN 13 | : 9780080533452 |

Language | : EN, FR, DE, ES & NL |

**Handbook of Evaluation Methods for Health Informatics Book Review:**

The Handbook of Evaluation Methods for Health Informatics provides a complete compendium of methods for evaluation of IT-based systems and solutions within healthcare. Emphasis is entirely on assessment of the IT-system within its organizational environment. The author provides a coherent and complete assessment of methods addressing interactions with and effects of technology at the organizational, psychological, and social levels. It offers an explanation of the terminology and theoretical foundations underlying the methodological analysis presented here. The author carefully guides the reader through the process of identifying relevant methods corresponding to specific information needs and conditions for carrying out the evaluation study. The Handbook takes a critical view by focusing on assumptions for application, tacit built-in perspectives of the methods as well as their perils and pitfalls. Collects a number of evaluation methods of medical informatics Addresses metrics and measures Includes an extensive list of anotated references, case studies, and a list of useful Web sites

## A Unifying Theory of Evolution Generated by Means of Information Modelling

Author | : J. Brender McNair |

Publsiher | : IOS Press |

Total Pages | : 236 |

Release | : 2016-09-13 |

ISBN 10 | : 1614996881 |

ISBN 13 | : 9781614996880 |

Language | : EN, FR, DE, ES & NL |

**A Unifying Theory of Evolution Generated by Means of Information Modelling Book Review:**

Stringent ways of thinking, ‘conceptual frameworks’, are necessary in science. The drawback is that the associated assumptions, concepts, rules and practice may become so deeply entrenched that they turn into tacit knowledge and hence give rise to constraints in scientific thought and practice – that is, a new kind of plethora that seriously blinds and thereby hampers scientific progress. This book, 'A Unifying Theory of Evolution Generated by Means of Information Modelling', presents a methodology for describing complex knowledge domains. It applies a template information model based on a dynamic structure of interrelated functions, called the Mereon Matrix. Application of this template model to the field of evolutionary theories enabled the unification of the sometimes chaotic and competing field of evolutionary theories, large and small, seamlessly in a shared framework. The author has Masters degrees in both biochemistry and computer science, as well as a European Doctorate and PhD in health informatics and has spent 35 years in full-time research. It is her particular combination of professional experience and expertise together with the template information model which has enabled her to write this book. Whilst primarily aimed at a scientific audience, and evolutionary biologists in particular, the book will be of interest to all those looking for new approaches to exploring and explaining phenomena in nature, and because the text is largely non-technical in nature, much of the content will also be accessible to a wider readership.

## The Pattern

Author | : Lynnclaire Dennis |

Publsiher | : Integral Pub |

Total Pages | : 183 |

Release | : 1997 |

ISBN 10 | : 9780941255509 |

ISBN 13 | : 0941255506 |

Language | : EN, FR, DE, ES & NL |

**The Pattern Book Review:**

This autobiographical account of a near-death experience is a powerful call for tolerance in today's multicultural society. What makes it so unusual and inspiring is that the provocative events described, and the "pattern" they imply, mark the first time since Newton that a cultural experience will affect -- even redefine -- science and technology. Dennis's story, told with disarming honesty and humor, has the power to change not only individual lives, but the very world in which we live.

## Methodology for Assessment of Medical IT based Systems

Author | : Jytte Brender |

Publsiher | : IOS Press |

Total Pages | : 295 |

Release | : 1997 |

ISBN 10 | : 9789051993370 |

ISBN 13 | : 9051993374 |

Language | : EN, FR, DE, ES & NL |

**Methodology for Assessment of Medical IT based Systems Book Review:**

10.2 The Role and Contents of the URD in an Assessment Perspective -- 10.3 The Enterprise Model -- 10.4 The Normative Model -- 10.5 Assessment of the User Requirements Document -- 10.6 Discussion -- 11 Dynamic Aspects of the Assessment Methodology -- 11.1 Dynamic Aspects of IT-Development and Application -- 11.2 Adaptation of Frames of Reference for Assessment Activities -- 11.3 Feed-forward Loops -- 11.4 Support of Context Dependent Assessment -- 11.5 Conclusion -- 12 The Dynamic Assessment Methodology -- 12.1 Philosophy -- 12.2 Application Area -- 12.3 Operationalisation of the Methodology -- 12.4 Applicable Methods -- 12.5 Summary -- 13 Discussion -- 13.1 Discussion of Fulfilment of Objective for the 4th Goal -- 13.2 Conclusion of the Study -- References -- Appendix 1: Vocabulary -- Appendix 2: Abbreviations & Acronyms -- Appendix 3: KAVAS's & ISAR's Evaluation Methodology -- Appendix 4: Methodology for Assessment of Functionality -- Appendix 5: Experimental Observations: Functionality Assessment -- Appendix 6: Experimental Observations: LFA -- Appendix 7: Causal Analysis of Experimental Observations -- Appendix 8: Method for Elicitation of a Strategy -- Appendix 9: Selected References regarding Assessment Methods

## On Knots

Author | : Louis H. Kauffman |

Publsiher | : Princeton University Press |

Total Pages | : 480 |

Release | : 1987 |

ISBN 10 | : 9780691084350 |

ISBN 13 | : 0691084351 |

Language | : EN, FR, DE, ES & NL |

**On Knots Book Review:**

On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.

## The Circle

Author | : Alfred S. Posamentier,Robert Geretschläger |

Publsiher | : Prometheus Books |

Total Pages | : 300 |

Release | : 2016-08-23 |

ISBN 10 | : 1633881687 |

ISBN 13 | : 9781633881686 |

Language | : EN, FR, DE, ES & NL |

**The Circle Book Review:**

The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson’s terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry—leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves – many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle’s place on the sphere bring "full circle" this presentation of a key element of geometry.

## Confident Parents Confident Kids

Author | : Jennifer S. Miller |

Publsiher | : Fair Winds Press |

Total Pages | : 192 |

Release | : 2019-11-05 |

ISBN 10 | : 1592339042 |

ISBN 13 | : 9781592339044 |

Language | : EN, FR, DE, ES & NL |

**Confident Parents Confident Kids Book Review:**

Confident Parents, Confident Kids lays out an approach for helping parents—and the kids they love—hone their emotional intelligence so that they can make wise choices, connect and communicate well with others (even when patience is thin), and become socially conscious and confident human beings. How do we raise a happy, confident kid? And how can we be confident that our parenting is preparing our child for success? Our confidence develops from understanding and having a mastery over our emotions (aka emotional intelligence)—and helping our children do the same. Like learning to play a musical instrument, we can fine-tune our ability to skillfully react to those crazy, wonderful, big feelings that naturally arise from our child’s constant growth and changes, moving from chaos to harmony. We want our children to trust that they can conquer any challenge with hard work and persistence; that they can love boundlessly; that they will find their unique sense of purpose; and they will act wisely in a complex world. This book shows you how. With author and educator Jennifer Miller as your supportive guide, you'll learn: the lies we’ve been told about emotions, how they shape our choices, and how we can reshape our parenting decisions in better alignment with our deepest values. how to identify the temperaments your child was born with so you can support those tendencies rather than fight them. how to align your biggest hopes and dreams for your kids with specific skills that can be practiced, along with new research to support those powerful connections. about each age and stage your child goes through and the range of learning opportunities available. how to identify and manage those big emotions (that only the parenting process can bring out in us!) and how to model emotional intelligence for your children. how to deal with the emotions and influences of your choir—the many outside individuals and communities who directly impact your child’s life, including school, the digital world, extended family, neighbors, and friends. Raising confident, centered, happy kids—while feeling the same way about yourself—is possible with Confident Parents, Confident Kids.

## Quantum Topology

Author | : Louis H. Kauffman,Randy A. Baadhio |

Publsiher | : World Scientific |

Total Pages | : 375 |

Release | : 1993 |

ISBN 10 | : 9789810225759 |

ISBN 13 | : 981022575X |

Language | : EN, FR, DE, ES & NL |

**Quantum Topology Book Review:**

This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.

## Virtual Knots

Author | : Vasiliĭ Olegovich Manturov,Denis Petrovich Ilyutko |

Publsiher | : World Scientific |

Total Pages | : 521 |

Release | : 2013 |

ISBN 10 | : 9814401129 |

ISBN 13 | : 9789814401128 |

Language | : EN, FR, DE, ES & NL |

**Virtual Knots Book Review:**

The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory. Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory. In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams. Graph-links can be treated as "diagramless knot theory": such "links" have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.

## Quantum Invariants

Author | : Tomotada Ohtsuki |

Publsiher | : World Scientific |

Total Pages | : 508 |

Release | : 2002 |

ISBN 10 | : 9789812811172 |

ISBN 13 | : 9812811176 |

Language | : EN, FR, DE, ES & NL |

**Quantum Invariants Book Review:**

This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."

## Knots and Applications

Author | : Louis H. Kauffman |

Publsiher | : World Scientific |

Total Pages | : 478 |

Release | : 1995 |

ISBN 10 | : 9789810220044 |

ISBN 13 | : 9810220049 |

Language | : EN, FR, DE, ES & NL |

**Knots and Applications Book Review:**

This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.

## Gaia

Author | : James Lovelock |

Publsiher | : Unknown |

Total Pages | : 148 |

Release | : 1995 |

ISBN 10 | : 9780192860309 |

ISBN 13 | : 0192860305 |

Language | : EN, FR, DE, ES & NL |

**Gaia Book Review:**

Contains a new preface written for this revised impression in which the author answers criticism for his ideas and underlines the continuing implications of this theory for the future -- Back cover.

## Dynamic Random Walks

Author | : Nadine Guillotin-Plantard,Rene Schott |

Publsiher | : Elsevier |

Total Pages | : 278 |

Release | : 2006-02-08 |

ISBN 10 | : 9780080462844 |

ISBN 13 | : 0080462847 |

Language | : EN, FR, DE, ES & NL |

**Dynamic Random Walks Book Review:**

The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!). · New probabilistic model, new results in probability theory · Original applications in computer science · Applications in mathematical physics · Applications in finance

## Combinatorial Physics

Author | : T Bastin,C W Kilmister |

Publsiher | : World Scientific |

Total Pages | : 188 |

Release | : 1995-08-31 |

ISBN 10 | : 9814500623 |

ISBN 13 | : 9789814500623 |

Language | : EN, FR, DE, ES & NL |

**Combinatorial Physics Book Review:**

The authors aim to reinstate a spirit of philosophical enquiry in physics. They abandon the intuitive continuum concepts and build up constructively a combinatorial mathematics of process. This radical change alone makes it possible to calculate the coupling constants of the fundamental fields which — via high energy scattering — are the bridge from the combinatorial world into dynamics. The untenable distinction between what is ‘observed’, or measured, and what is not, upon which current quantum theory is based, is not needed. If we are to speak of mind, this has to be present — albeit in primitive form — at the most basic level, and not to be dragged in at one arbitrary point to avoid the difficulties about quantum observation. There is a growing literature on information-theoretic models for physics, but hitherto the two disciplines have gone in parallel. In this book they interact vitally. Contents: Introduction and Summary of ChaptersSpaceComplementarity and All ThatThe Simple Case for a Combinatorial PhysicsA Hierarchical Model — Some Introductory ArgumentsA Hierarchical Combinatorial Model — Full TreatmentScattering and Coupling ConstantsQuantum Numbers and the ParticleToward the ContinuumObjectivity and Subjectivity — Some ‘ISMS’ Readership: Graduates, mathematical physicists, high energy physicists, philosophers of science and information theorists. keywords:Quantum Physics;Fine Structure Constant;Dimensionless Constants;Process;Discrete Physics;Combinatorics;Eddington;Hierarchies

## Cymatics

Author | : Hans Jenny |

Publsiher | : Macromedia |

Total Pages | : 295 |

Release | : 2001 |

ISBN 10 | : 9781888138078 |

ISBN 13 | : 1888138076 |

Language | : EN, FR, DE, ES & NL |

**Cymatics Book Review:**

Cymatics is the study of sound-wave phenomena and this astonishing book vividly depicts the significance of audible sound throughout our world. It presents, primarily through beautiful colour photographs, the effects of sound vibrations to excite powders, pastes and liquids into life-like, flowing forms. The resultant patterns can be found throughout nature, art and architecture.This new edition contains the complete English text of both of Hans Jenny’s original bilingual volumes, together with all the photographs, as well as a new introduction and commentary to the work. The book is essential reading for students of sacred geometry, mandalas, metaphysics, sound healing and even crop circles.

## Little Book of Coincidence

Author | : John Martineau |

Publsiher | : eBook Partnership |

Total Pages | : 64 |

Release | : 2018-04-01 |

ISBN 10 | : 1912706075 |

ISBN 13 | : 9781912706075 |

Language | : EN, FR, DE, ES & NL |

**Little Book of Coincidence Book Review:**

Venus draws a beautiful pentagram around Earth every eight years. Jupiter's two largest moons draw a perfect four-fold flower. The Planets grandly play out the slow Music of the Spheres. Is there a secret structure hidden in the Solar System? Packed with great illustrations and serious research from many sources, this internationally bestselling little book by cosmologist John Martineau will instantly retune your cosmological circuits to the extraordinary and primary patterns behind Life, the Universe and Everything. WOODEN BOOKS are small but packed with information. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.

## Symmetries And Curvature Structure In General Relativity

Author | : Hall Graham S |

Publsiher | : World Scientific |

Total Pages | : 440 |

Release | : 2004-04-27 |

ISBN 10 | : 9814505315 |

ISBN 13 | : 9789814505314 |

Language | : EN, FR, DE, ES & NL |

**Symmetries And Curvature Structure In General Relativity Book Review:**

This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.