Last updated June 21, 2001 |

- Symplectic and Poisson manifolds. The Darboux theorem.
- Finite-dimensional Hamiltonian formalism. Integrable Hamiltonian systems.
- The Schouten bracket. Deformations and the Hamiltonian cohomology. An algebraic model for the Poisson geometry.
- Jet bundles. The spectral sequence of an integrable distribution. The one-line theorem: variational complex.
- Infinite-dimensional Hamiltonian systems.
- The symmetries and conservation laws of Hamiltonian equations. The integrability of infinite-dimensional systems.
- Bi-Hamiltonian equations: the Magri theorem and hierarchies of soliton equations.
- Examples and perspectives.

Questions and suggestions should go to J. S. Krasil'shchik, josephk @ diffiety.ac.ru.