Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.

The McKay conjecture is the origin of the counting conjectures in the representation theory of finite groups. This book gives a comprehensive introduction to th

Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fiel

Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century.

The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's disti