Chapter 1. Introduction -- 1.1 Quantum physics and classical electromagnetism -- 1.2 Abelian Chern-Simons action -- 1.3 Non-Abelian Chern-Simons action -- Chapter 2. Basic notions of knot theory -- 2.1 Ambient and regular isotopy -- 2.2 Link invariants -- 2.3 Framing and satellites -- Chapter 3. Framing in field theory -- 3.1 Abelian Chern-Simons theory -- 3.2 Framed Wilson line operators -- Chapter 4. Non-Abelian Chern-Simons theory -- 4.1 Covariant quantization -- 4.2 One-loop effective action -- 4.3 Higher order results -- Chapter 5. Observables and perturbation theory -- 5.1 Wilson line operators -- 5.2 Perturbative computations -- Chapter 6. Properties of the expectation values -- 6.1 Holonomy matrix -- 6.2 Discrete symmetries -- 6.3 Satellite formulae -- Chapter 7. Ordering fermions and knot observables -- 7.1 Ordering fermions -- 7.2 Antiperiodic boundary conditions -- 7.3 Knot observables -- Chapter 8. Braid group -- 8.1 Artin braid group -- 8.2 Hecke algebra -- Chapter 9. R-matrix and braids -- 9.1 Quantum group approach -- 9.2 Lie algebras and monodromy representations -- 9.3 Quasi-Hopf algebra -- Chapter 10. Chern-Simons monodromies -- 10.1 Schrödinger picture -- 10.2 Universality of the link invariants -- 10.3 The inexistent shift -- Chapter 11. Defining relations -- 11.1 Calculus rules -- Chapter 12. The extended Jones polynomial -- 12.1 The values of the unknots -- 12.2 Hopf link -- 12.3 Trefoil knot -- 12.4 Figure-eight knot -- 12.5 Connection with the Jones polynomial -- 12.6 Bracket connection -- 12.7 Reconstruction theorems -- Chapter 13. General properties -- 13.1 Twist variable -- 13.2 Recovered field theory -- 13.3 Links in a solid torus -- 13.4 Satellites -- 13.5 Skein relation -- 13.6 Projectors -- 13.7 Borromean rings -- 13.8 Connected sums -- 13.9 Mutations -- Chapter 14. Unitary groups -- 14.1 Fundamental skein relation.

14.2 Casimir operator -- 14.3 Composite states -- 14.4 Pattern links -- 14.5 Higher dimensional representations -- 14.6 Polynomial structure -- 14.7 SU(3) examples -- Chapter 15. Reduced tensor algebra -- 15.1 The restated solution -- 15.2 Outlook -- 15.3 Representation ring -- 15.4 The three-sphere -- 15.5 Reduced tensor algebra -- 15.6 Roots of unity -- 15.7 Special cases -- Chapter 16. Surgery on three-manifolds -- 16.1 Mapping class group of the torus -- 16.2 Solid tori -- 16.3 Dehn surgery -- 16.4 Links in three-manifolds -- 16.5 Elementary surgeries -- 16.6 Physical interpretation -- 16.7 The fundamental group -- Chapter 17. Surgery and field theory -- 17.1 Basic pairing -- 17.2 Properties of the Hopf matrix -- 17.3 Elementary surgery operators -- 17.4 Surgery operator -- 17.5 Surgery rules and Kirby moves -- Chapter 18. Observables in three-manifolds -- 18.1 The manifold S2 × S1 -- 18.2 The manifold RP3 -- 18.3 Lens spaces -- 18.4 The Poincaré manifold -- 18.5 The manifold T2 S1 -- Chapter 19. Three-manifold invariant -- 19.1 Improved partition function -- 19.2 Values of the invariant -- Chapter 20. Abelian surgery invariant -- 20.1 Compact Abelian theory -- 20.2 Abelian surgery rules -- 20.3 Abelian surgery invariant -- References -- Subject Index.