This is a comprehensive introduction to the modular representation
theory of finite groups, with an emphasis on block theory. The two
volumes take into account classical results and concepts as well as
some of the modern developments in the area. Volume 1 introduces
the broader context, starting with general properties of finite
group algebras over commutative rings, moving on to some basics in
character theory and the structure theory of algebras over complete
discrete valuation rings. In Volume 2, blocks of finite group
algebras over complete p-local rings take centre stage, and many
key results which have not appeared in a book before are treated in
detail. In order to illustrate the wide range of techniques in
block theory, the book concludes with chapters classifying the
source algebras of blocks with cyclic and Klein four defect groups,
and relating these classifications to the open conjectures that
drive block theory.
General
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