Train track course

Background. Good sources of information are the following books:

Massey: Algebraic topology: an introduction, Springer-Verlag
Hatcher: Algebraic Topology, Cambridge University Press, available online here

Massey's book is more elementary and is commonly used for an undergraduate topology course. Hatcher's book is more extensive but we will only need a subset of Chaper 1.

Here is a list of particular topics you should have some familiarity with. We will review these concepts as needed. To get you started, here is a little handout. After this, you can read the notes about free groups by John Stallings. He was a real master of the subject and came up with many cool things, including folding of graphs that we will talk about.

Free groups. Massey, Ch 3, sections 4,5 and Hatcher pp 41-42. (Or read the handout and the notes above.)
Fundamental group. Massey Ch 2, section 2, Hatcher 1.1.
The fundamental group of a graph is free. This is a very special case of the Seifer-Van Kampen theorem (Massey Ch 4, Hatcher 1.2)
Surfaces. Massey Ch 1, particularly section 5.
Covering spaces. Particularly that the universal cover of a graph is a tree (usually infinite). Massey Ch 5, section 4, Hatcher 1.3.

Links to notes for topics covered in the course:

Notes by Professor Caroline Series at the University of Warwick on hyperbolic geometry.
A nice and short proof, by Borobia-Trias, of the Perron-Frobenius theorem.
There are many books on dynamics, they usually have the word "ergodic" in the title. The following web page contains a lot of information and looks very accessible. Check out the sections "More on topological entropy" and "symbolic coding".
Here are my notes for a graduate class where I talked about the Stallings' paper Topology of finite graphs. The notes contain some exercises you can think about.
Notes on Outer space, from my lectures in 2012 at the Park City Math Institute.
Software, by Thierry Coulbois, based on sage, that can compute train tracks.

Exercises:

Exercises about SL₂(R), dynamics and train tracks.
Chris's exercises about hyperbolic geometry.
There are exercises in the notes under bullets 4 and 5 above.