1. Chern classes and the Riemann-Roch theorem for projective surfaces.
2. Topology and geometry of K3 surfaces.
3. Holomorphically symplectic geometry. Hyperkahler structures.
4. Local and global Torelli theorem. All K3 surfaces are diffeomorphic.
5 *. Examples of K3 surfaces. Automorphism group and the shape Kahler cone.
6 *. Nakai-Moishezon theorem. Classification of automorphisms and their dynamics.
7 *. Ergodic action on the Teichmuller space of K3 surfaces. Kobayashi metric and Kobayashi hyperbolic manifolds. Non-hyperbolicity of K3 surfaces.