Lecture 2: Pick's theorem on interpolation by holomorphic functions mapping the unit disc into itself.

Lecture 3: Angular derivative, Denjoy-Wolff theorem.

Lecture 4: Ahlfors's generalization of Schwarz's Lemma, Bloch's theorem. Theorems of Picard and Nevanlinna (after Robinson).

Lecture 5: Topological preliminaries: coverings and fundamental group. Surfaces and Riemann surfaces.

Lecture 6: Uniformization. Classification of Riemann surfaces. Hyperbolic Riemann surfaces.

Lecture 7: Normal families and Montel's theorem. Iteration of rational functions.

Lecture 8: Dynamics on hyperbolic surfaces, classification of invariant domains for rational functions.

Lecture 9: Fuchsian groups, fundamental regions and Poincare theorem.