The theme of this textbook is quantum physics of systems consisting of a large number of particles. A book in the form of a collection of problems allows you to consider the main theoretical methods of this section of physics and at the same time cover a wide range of specific physical phenomena. The problems of the first part of the book are selected so that, using the example of material known to the reader on non-relativistic quantum mechanics, illustrate the method of Green's functions. Problems are accompanied by detailed solutions and comments explaining the motivation and connection with various issues of modern condensed matter theory.