The aim of this book is to serve both as an introduction to profinite
groups and as a reference for specialists in some areas of the theory.
The book is reasonably self-contained. Profinite groups are Galois
groups. As such they are of interest in algebraic number theory. Much of
recent research on abstract infinite groups is related to profinite
groups because residually finite groups are naturally embedded in a
profinite group. In addition to basic facts about general profinite
groups, the book emphasizes free constructions (particularly free
profinite groups and the structure of their subgroups). Homology and
cohomology is described with a minimum of prerequisites.
This second edition contains three new appendices dealing with a new
characterization of free profinite groups, presentations of pro-p groups
and a new conceptually simpler approach to the proof of some classical
subgroup theorems. Throughout the text there are additions in the form
of new results, improved proofs, typographical corrections, and an
enlarged bibliography. The list of open questions has been updated;
comments and references have been added about those previously open
problems that have been solved after the first edition appeared.