Lectures on Symplectic Manifolds

Introduction Symplectic manifolds and lagrangian submanifolds, examples Lagrangian splittings, real and complex polarizations, Kahler manifolds Reduction, the calculus of canonical relations, intermediate polarizations Hamiltonian systems and group actions on symplectic manifolds Normal forms Lagrangian submanifolds and families of functions Intersection theory of lagrangian submanifolds Quantization on cotangent bundles Quantization and polarizations Quantizing lagrangian submanifolds and subspaces, construction of the Maslov bundle References.