Описание:The course gives a comprehensive introduction into the basics of symplectic geometry and quantization. These deeply interrelated subjects provide a geometrical insight into the classical and quantum description of fundamental physical systems. We begin with basic structures of symplectic geometry such as Poisson brackets, hamiltonian fields, momentum maps, Atiyah-Bott theory etc. and their properties. After this we give an introduction to the concept of quantization in general and illustrate it by standard simple examples. A particular attention is paid to the concept of symbols and deformations. We then consider Fedosov’s construction of deformation quantization of general symplectic manifolds. Finally, a more general approach of Kontsevich is presented together with the elements of general deformation theory such as Hochschild cohomology, homotopy algebras etc.