Poisson manifolds: Poisson and Schouten brackets. Symplectic foliation and transverse Poisson structure. Poisson calculus. Modular class. Symplectic realizations. Poisson cohomology and Lie algebra cohomology. Normal forms for Poisson structures: Levi decomposition, linear approximation to Poisson structures, nondegenerate Lie algebras. Introduction to the study of Lie algebroids.
