NIP and definably amenable groups

Abstract

This text is an introduction to definably amenable NIP groups. It is based on a number of papers, mainly [6], [7] and [4]. This subject has two origins, the first one is the theory of stable groups and in particular generic types, which were first defined by Poizat (see [12]) and have since played a central role throughout stability theory. Later, part of the theory was generalized to groups in simple theories, where generic types are dened as types, none of whose translates forks over the empty set.