This is a course on the main notions and basic facts of symplectic topology. The topics to be covered include: symplectic and contact spaces, Morse theory, generating functions for symplectomorphisms, symplectic fixed point theorems (Arnold's conjectures), and invariants of legendrian knots. We also plan to touch on almost complex structures, groups of symplectomorphisms, definitions of symplectic capacities and Floer homology. In the second part of the course we are going to cover various constructions of completely integrable systems in finite and infinite dimensions. An acquaintance with basic symplectic geometry (e.g. covered by MAT 1344HF, Introduction to Symplectic Geometry) is advisable.

References:
S.Tabachnikov: Introduction to symplectic topology (Lecture notes, PennState U.)
D.McDuff and D.Salamon: Introduction to symplectic topology (Oxford Math. Monographs, 1998)
A.Perelomov: Integrable systems of classical mechanics and Lie algebras (Birkhauser, 1990)