This book is an introduction to the techniques of quantum theory of many-particle systems with applications in condensed matter physics. The basic principles of quantum mechanics are the starting point for the development of the language of second quantization, which is used to introduce and analyze a series of basic models of interacting particles. An extensive presentation of the theory of Green's functions follows, which are directly related to the observable quantities of physical systems at finite temperatures. In this context, the method of motion equations and the technique of Feynman diagrams are developed, which are the main computational tools for Green's functions. Applications include, among others, basic aspects of phenomena such as superfluidity, superconductivity, and magnetism.

The book is aimed at graduate and advanced undergraduate students who wish to understand the behavior of many-particle systems based on the principles of quantum mechanics and statistical mechanics. Additionally, it is intended to be useful for researchers in the field as a reference for the techniques it deals with.