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This book presents a comprehensive and detailed exposition of the fundamentals of the representation theory of groups, especially of finite groups and compact groups. The exposition is based on the decomposition of the two-sided regular representation.

This is a quite extraordinary book on Lie groups and algebraic groups. Created from hectographed notes in Russian from Moscow University, which for many Soviet mathematicians have been something akin to a "bible," the book has been substantially extended and organized to develop the material through the posing of problems and to illustrate it through a wealth of examples. Several tables have never before been published, such as decomposition of representations into irreducible components. This will be especially helpful for physicists. The authors have managed to present some vast topics: the...

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.

Editorial Board

Lev Birbrair,...