These are notes of the mini-courses we lectured in Trieste in 2003 and Luminy in 2004. The courses were based on the books [1, 3, 2]. 1 Symplectic and contact geometry 1.1 Symplectic geometry A symplectic form ω on a manifold M is a closed 2-form, non-degenerate as a skew-symmetric bilinear form on the tangent space at each point. So dω = 0 and ω n is a volume form, dim M = 2n. Manifold M equipped with a symplectic form is called symplectic. It is necessarily evendimensional.