The course begins with a consideration of systems of non-interacting particles - bosons and fermions, their statistics, and the difficulties of using traditional perturbation theory when taking into account the interaction between particles. Then traditional single-particle methods are discussed, such as the Thomas-Fermi method, the local density approximation, the Hartree-Fock approximation. Much attention is paid to the density functional theory, in particular, the local density approximation, as it is widely used in calculations of many-electron systems. The subsequent part of the course examines in detail the field methods of many-body theory: secondary quantization, interaction representation, field operators, Green's functions, diagram technique. The last part of the course is devoted to the application of the Feynman and Goldstone diagram technique for calculating the structure and processes of interaction of many-body systems with an electromagnetic field and other particles.