This volume exposes the theory of biset functors for finite groups which yields a unified
framework for operations of induction restriction inflation deflation and transport by
isomorphism. The first part recalls the basics on biset categories and biset functors. The
second part is concerned with the Burnside functor and the functor of complex characters
together with semisimplicity issues and an overview of Green biset functors. The last part is
devoted to biset functors defined over p-groups for a fixed prime number p. This includes the
structure of the functor of rational representations and rational p-biset functors. The last
two chapters expose three applications of biset functors to long-standing open problems in
particular the structure of the Dade group of an arbitrary finite p-group.This book is intended
both to students and researchers as it gives a didactic exposition of the basics and a
rewriting of advanced results in the area with some new ideas and proofs.
