**Synopsis:**
I plan to cover the following topics, listed in the order of their appearance in lectures.

- The Banach-Tarski Paradox.

- Amenable graphs, Amenable groups: equivalent definitions, stability under group operations.

- The von Neumann-Day conjecture, Jacques Tits' Alternative Theorem for linear groups.

Recommended reference for algebraic groups (unfortunately out of print): the book of Onishchik and Vinberg.

**Lecture notes: **

Exercise Sheet 1. For any type of assessment (broadening courses or others) answers must be sent in by email before June 12 (details on the sheet).