This 1996 book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang–Baxter algebras and the Bethe ansatz. The basic ideas of integrable systems are then introduced, giving particular emphasis to vertex and face models. Special attention is given to explaining the underlying mathematical tools, including braid groups, knot invariants and towers of algebra. The book then goes on to give a detailed introduction to quantum groups as a prelude to chapters on integrable models, two-dimensional conformal field theories and superconformal field theories. The book contains many diagrams and exercises to illustrate key points in the text.

"The book is written in a simple and lucid manner, that allows one to suggest it for an audience with no previous acquaintance with the subject. This book will be of use to graduate students and researchers in theoretical physics and applied mathematics interested in integrable systems, string theory and conformal field theory." Audrey V. Tsiganov, Mathematical Reviews