After the pioneering work of Brauer in the middle of the 20th century, many new developments have taken place and the group representation theory has grown into a very large field of study. This progress and the remaining open problems have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: finite reductive groups and spetses; cohomology and representations of finite groups; representations of Hecke algebras; topics in algebraic groups; fusion systems and blocks; finite subgroups of Lie groups; the classification of endo-permutation modules; and rand cohomology of categories.