Quantum and related invariants of knots and 3-manifolds are presented, and polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants derived from representation of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. Discussion encompasses the Kontsevich invariants, the theory of Vassiliev invariants, the LMO invariants, and finite type invariants of 3-manifolds. The Chern- Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants. The author is affiliated with the Tokyo Institute of Technology, Japan. Annotation c. Book News, Inc., Portland, OR (booknews.com)