1. KP hierarchy and infinite-dimensional grassmannians. Main classes of solutions: solitons, quasi-periodic solutions, rational solutions and bispectrality.

2. Symmetries and reductions of KP and of multicomponent KP.

3. Hamiltonian structures of 1+1 and 1+0 integrable systems. Algebraic-geometrical action-angle variable.

4. Integrable systems and Dynkin diagrams: Drinfeld-Sokolov classification.