Group theory is one of the most fundamental branches of
mathematics. This volume of the Encyclopaedia is devoted to
two important subjects within group theory. The first part
of the book is concerned with infinite groups. The authors
deal with combinatorial group theory, free constructions
through group actions on trees, algorithmic problems,
periodic groups and the Burnside problem, and the structure
theory for Abelian, soluble and nilpotent groups. They have
included the very latest developments; however, the material
is accessible to readers familiar with the basic concepts of
algebra.
The second part treats the theory of linear groups. It is a
genuinely encyclopaedic survey written for non-specialists.
The topics covered includethe classical groups, algebraic
groups, topological methods, conjugacy theorems, and finite
linear groups.
This book will be very useful to allmathematicians,
physicists and other scientists including graduate students
who use group theory in their work.

Translated by: J. Wiegold
Contributions by: A.Yu. Ol'shanskij, A.L. Shmel'kin, A.E. Zalesskij