Green Functors and G sets This book provides a definition of Green functors for a finite group G and of modules over it in terms of the category of finite G sets. Some classical constructions such as the associated categroy or algebra have a natural interpretation in that framework. Many notions of ring theory can be extended to Green functors (opposite Green functor bimodules Morita theory simple modules centres ..). There are moreover connections between Green functors for different groups given by functors associated to bisets. Intended for researchers and students in representation theory of finite groups it requires only basic algebra and category theory though knowledge of the classical examples of Mackey functors is probably preferable