2nd semester
20 credits / 30 lectures

The course will focus on a the theory of topological groups, focusing on the compact groups and discussing the related Lie Theory.
The suggested textbook is

K.H.Hofmann and S.Morris, The Structure of Compact Groups, de Gruyter, Berlin, 2006.

Of course, any other edition of this book is fine. The main idea is to cover the first seven chapters, integrating with the appendices when necessary. The contents will be:

1. Basic notions and examples of topological groups.
2. Haar measure and basic representation theory of compact groups.
3. The theorem of Peter and Weyl.
4. Elementary notions of character theory of compact groups.
5. Compact Lie groups and linear Lie groups.