In 1999 a number of eminent mathematicians were invited to Bielefeld, to present papers at a one-week conference devoted to interactions between (mostly) infinite groups on the one hand and topological, combinatorial and arithmetic structure on the other. The present volume consists of articles invited from participants in this conference.

A glance at the table of contents gives an immediate impression of the breadth and depth of the contributions included here. The study of topological finiteness properties, a beautiful field of research inhabiting the fertile region between group theory and geometry, is the subject matter of papers by Abramenko, Behr, and Bux, while the article by Bieri and Geoghegan extends this theme towards a theory of group actions on non-positively curved spaces. Another exciting topic of somewhat similar geometric flavour is the theory of Kac-Moody groups, of which Remy's article gives a timely and masterly exposition, incorporating much of his own research. The paper by Chiswell, almost a monograph on its own provides a surprisingly accessible and highly readable account of the theory of Euler characteristics, an account which had been sorely missed in the literature.

The papers by Nekrashevych and Sidki and by Parker and Series both explore the fruitful connection between groups and inherent geometric structure on the one hand, and formal languages and automata on the other.