**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).

Exercise Sheet 2. For any type of assessment (broadening courses or others) answers must be sent in by email before June 28 (details on the sheet).