Table of Contents -- Preface to the First Edition -- Preface to the Second Edition -- Preface to the Third Edition -- PART I. A SHORT COURSE OF KNOTS AND PHYSICS. -- 1°. Physical Knots. -- 2°. Diagrams and Moves. -- 3°. States and the Bracket Polynomial. -- 4°. Alternating Links and Checkerboard Surfaces. -- 5°. The Jones Polynomial and its Generalizations. -- 6°. An Oriented State Model for VK(t). -- 7°. Braids and the Jones Polynomial. -- 8°. Abstract Tensors and the Yang-Baxter Equation. -- 9°. Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q. -- 10°. The Form of the Universal R-matrix. -- 11°. Yang-Baxter Models for Specializations of the Homfly Polynomial. -- 12°. The Alexander Polynomial. -- 13°. Knot-Crystals - Classical Knot Theory in Modern Guise. -- 14°. The Kauffman Polynomial. -- 15°. Oriented Models and Piecewise Linear Models. -- 16°. Three Manifold Invariants from the Jones Polynomial. -- 17°. Integral Heuristics and Witten's Invariants. -- 18°. Appendix - Solutions to the Yang-Baxter Equation. -- PART II. KNOTS AND PHYSICS - MISCELLANY. -- 1°. Theory of Hitches. -- 2°. The Rubber Band and Twisted Tube. -- 3°. On a Crossing. -- 4°. Slide Equivalence. -- 5°. Unoriented Diagrams and Linking Numbers. -- 6°. The Penrose Chromatic Recursion. -- 7°. The Chromatic Polynomial. -- 8°. The Potts Model and the Dichromatic Polynomial. -- 9°. Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum. -- 10°. Quaternions, Cayley Numbers and the Belt Trick. -- 11°. The Quaternion Demonstrator. -- 12°. The Penrose Theory of Spin Networks. -- 13°. Q-Spin Networks and the Magic Weave. -- 14°. Knots and Strings - Knotted Strings. -- 15°. DNA and Quantum Field Theory. -- 16°. Knots in Dynamical Systems - The Lorenz Attractor. -- CODA. -- REFERENCES -- Index -- APPENDIX -- Introduction.

First Article -- Second Article -- Third Article -- Fourth Article -- Gauss Codes, Quantum Groups and Ribbon Hopf Algebras -- I. Introduction -- II. Knots and the Gauss Code -- III. Jordan Curves and Immersed Plane Curves -- IV. The Abstract Tensor Model for Link Invariants -- V. From Abstract Tensors to Quantum Algebras -- VI. From Quantum Algebra to Quantum Groups -- VII. Categories -- VIII. Invariants of 3-Manifolds -- IX. Epilogue -- Spin Networks, Topology and Discrete Physics -- I. Introduction -- II. Trees and Four Colors -- III. The Temperley Lieb Algebra -- IV. Temperley Lieb Recoupling Theory -- V. Penrose Spin Networks -- VI. Knots and 3-Manifolds -- VII. The Shadow World -- VIII. The Invariants of Ooguri, Crane and Yetter -- LINK POLYNOMIALS AND A GRAPHICAL CALCULUS -- 0. Introduction -- 1. Rigid Vertex Isotopy -- 2. The Homfly Polynomial -- 3. Braids and the Hecke Algebra -- 4. Demonstration of Identities in Oriented Graphical Calculus -- 5. The Dubrovnik Polynomial -- Knots, Tangles, and Electrical Networks -- 1. INTRODUCTION -- 2. KNOTS, TANGLES, AND GRAPHS -- 3. CLASSICAL ELECTRICITY -- 4. MODERN ELECTRICITY - THE CONDUCTANCE INVARIANT -- 5. TOPOLOGY: MIRROR IMAGES, TANGLES AND CONTINUED FRACTIONS -- 6. CLASSICAL TOPOLOGY -- Knot Theory and Functional Integration -- 1 Introduction -- 2 Vassiliev Invariants and Invariants of Rigid Vertex Graphs -- 3 Vassiliev Invariants and Witten's Functional Integral -- 4 Gaussian Integrals -- 5 The Three-Dimensional Perturbative Expansion -- 6 Wilson Lines, Light-Cone Gauge and the Kontsevich Integrals -- 7 Formal Integration.