Before 1950 there was practically no many-body problem. Only some precursors had touched on the study of condensed systems. Their efforts remained isolated and elicited little response from the main body of physicists. In ten years this subject has been developed to such a point that it is now involved in every area of physics. The first efforts in this direction were quite disconnected. Several approximate theories were proposed, each of which treated a very specialized subject. This diversity is manifest in the courses offered at the 1958 session of the Summer School of Theoretical Physics at Les Houches. The essential step has been to set up a unified formalism, based on the methods of quantum field theory. The same "language" now allows us to treat nuclear matter, liquid helium, or superconductors. These new methods also possess a great virtue - they can be generalized to systems at finite temperatures; the many-body problem thus becomes allied with quantum statistical mechanics, representing the latter's low-temperature limit. These new paths seem extremely promising. There is no question of covering so vast a subject within the framework