Quantum Invariants of Knots and 3-Manifolds

This monograph provides a systematic treatment of topological quantum field theories (TQFT's) in three dimensions, inspired by the discovery of the Jones polynomial of knots, the Witten-Chern-Simons field theory, and the theory of quantum groups. The author, one of the leading experts in the subject, gives a rigorous and self-contained exposition of new fundamental algebraic and topological concepts that emerged in this theory.