Combinatorial Group Theory is a field encompassing different topics in the theory of infininte groups, in which the questions and/or tools have combinatorial flavor. We shall study most of the following subjects (the exact content of the class will be determined along the semester):

1. The basics: presentation of groups by generators and relations and basic questions such as the word problem, the conjugacy problem and the automorphism problem.

2. Free groups: Stallings core graphs, Nielsen-Schreier thm, the automorphism group, primitive elements, Whitehead solution of the isomorphism problem

3. Basse-Serre Theory: groups acting on trees, amalgamated products, HNN extensions

4. Small cnacelation groups

Other possible topics: growth of groups, amenability of discrete groups, Hanna-Neumann conjecture and its solution, Baumslag-Solitar groups