At the crossroads of representation theory, algebraic geometry and finite group theory, this book brings together many of the main concerns of modern algebra, synthesizing the past twenty-five years of research, by including some of the most remarkable achievements in the field. The text is illustrated throughout by many examples, and background material is provided by several introductory chapters on basic results as well as appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and a reference for all algebraists.

Finite reductive groups and their representations lie at the heart of group theory. This volume treats linear representations of finite reductive groups and their modular aspects together with Hecke algebras, complex reflection groups, quantum groups, arithmetic groups, Lie groups, symmetric groups and general finite groups.