- Basic Results concerning Topological Spaces (4 lectures?)
- Winding Numbers and Monodromy
- Fundamental Groups of Topological Spaces
- Covering Maps
- Discontinuous Group Actions (?)

Study Week

- Topology and geometry of surfaces (possibly including the Gauss-Bonnet Theorem and/or the two-dimensional case of the Poincaré-Hopf Theorem
- Topological Classification of Closed Surfaces
- Further examples?