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In 1999 a number of eminent mathematicians were invited to
Bielefeld to present lectures at a conference on topological,
combinatorial and arithmetic aspects of (infinite) groups. The
present volume consists of survey and research articles invited
from participants in this conference. Topics covered include
topological finiteness properties of groups, Kac-Moody groups, the
theory of Euler characteristics, the connection between groups,
formal languages and automata, the Magnus-Nielsen method for
one-relator groups, atomic and just infinite groups, topology in
permutation groups, probabilistic group theory, the theory of
subgroup growth, hyperbolic lattices in dimension three,
generalised triangle groups and reduction theory. All contributions
are written in a relaxed and attractive style, accessible not only
to specialists, but also to good graduate and post-graduate
students, who will find inspiration for a number of basic research
projects at various levels of technical difficulty.
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