The ICMS Workshop on Geometric and Combinatorial Methods in Group Theory, held at Heriot-Watt University in 1993, brought together some of the leading research workers in the subject. Some of the survey articles and contributed papers presented at the meeting are collected in this volume. The former cover a number of areas of current interest and include papers by: S. M. Gersten, R. I. Grigorchuk, P. H. Kropholler, A. Lubotzky, A. A. Razborov and E. Zelmanov. The contributed articles, all refereed, range over a wide number of topics in combinatorial and geometric group theory and related topics. The volume represents a summary of the state of knowledge of the field, and as such will be indispensable to all research workers in the area.

The main theme of this book is the mathematical theory of knots and its interaction with the theory of surfaces. Beginning with a simple diagrammatic approach to the study of knots, reflecting the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent advances in our understanding to areas of current research. Included are straightforward introductions to topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations. These topics combine into a coherent and highly developed theory to explore and explain the accessible and intuitive problems of knots and surfaces. Both as an introduction to several areas of prime importance to the development of pure mathematics today, and as an account of pure mathematics in action in an unusual context, the book presents novel challenges to students and other interested readers.