We will study the groups Aut(F_n), Out(F_n) and related groups via their actions on contractible spaces which can be described in terms of finite metric graphs, sphere systems in a doubled handlebody or actions of F_n on trees. After a basic introduction to these groups and spaces we will concentrate on tools that are used to study their geometry and topology. Topological information includes constructing homology classes, proving a type of duality between homology and cohomology, and determining the rational Euler characteristic. For geometry we will describe an asymmetric metric and see how it can be used to construct nice representatives for automorphisms.

Resources

Here are my 2015 TCC course notes