The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

**Title**: Ergodic theory and amenable groups

**Lecturer**: Benjamin Weiss

**Date**: October 31, 2016.

**Main Topics**: Three equivalent notions of amenability, Basic concepts in ergodic actions, Furstenberg’s Ergodic proof of Szemerédi’s theorem

**Definitions:** Ergodic action, weak mixing, mixing, Banach limit, amenable group, left invariant mean, paradoxical decomposition, Følner sequence