This concise monograph is devoted to techniques of solving many-body problems in physics using the quantum-mechanical Green function method. Suitable for advanced undergraduates and graduate students of physics, it requires some familiarity with the basic theory of quantum mechanics and statistical mechanics.Focusing on the general method, the treatment begins by establishing the connection between the Green functions and the thermodynamic and kinetic characteristics of a system. Subsequent chapters illustrate the method and apply it to different problems in the physics of condensed media, including the theory of electron plasmas in solids, electron-phonon interactions, and ferromagnetism at finite temperatures. Seven helpful Appendixes offer supplementary information. Reprint of the North-Holland Publishing Company, Amsterdam, 1962 edition.