The physical foundations and mathematical apparatus of quantum theory, nonrelativistic and quasi-relativistic motion of particles in an external magnetic field, the theory of systems of identical interacting particles and a description of various quantum phenomena are given. Much attention is paid to the theory of representation of groups, the theory of unitary transformations, the theory of scattering, and the theory of quantum transitions. The methods for describing quantum systems using filling numbers (secondary quantization method), Green's functions and density matrix are given, as well as the basis of the theory of irreversible processes and the theory of coherent states. The important for practical application Bogolyubov-Tiablikov's canonical transformation and the question of interaction of electromagnetic radiation and particles with matter are considered in detail. For students of classical and technical universities.