Lionel Nguyen Van Thé: An introduction to the Kechris-Pestov-Todorcevic correspondence.

In 2005, Kechris, Pestov and Todorcevic established a surprising correspondence between structural Ramsey theory and topological dynamics, which triggered a new interest for the former of these fields. The purpose of this series of lectures is to present a self-contained introduction of this correspondence and of some of the developments that followed.