1. General notion of a homotopy invariant of topological spaces.
3. The coverings and the fundamental group; examples of computation; Van Kampen theorem.
4. The higher homotopy groups: easy to define but hard (in general impossible) to compute.
5. The homology and cohomology groups: harder to define but computable.
6. Computation of H(S^n), degree of a map.
7. The Euler characteristic of a triangulated space, independence on triangulation, the Lefschetz fixed-pont theorem, Hopf theorem on zeroes on a vector field on a manifold.