1 Preliminaries
2 Basic topological properties of finite spaces
3 Minimal finite models
4 Simple homotopy types and finite spaces
5 Strong homotopy types
6 Methods of reduction
7 h-regular complexes and quotients
8 Group actions and a conjecture of Quillen
9 Reduced lattices
10 Fixed points and the Lefschetz number
11 The Andrews-Curtis conjecture.