This book thoroughly describes our present theoretical knowledge of the nuclear many-body problem. It also covers more standard topics such as the liquid drop model, shell model, rotations and pairing theory. Emphasis is put on the methodology and technical aspects of modern theories and concepts such as small and large amplitude collective motion, boson expansions, generator coordinates, time-dependent Hartree-Fock theory, broken symmetries and semiclassical approximations, which have, up to now, received limited detailed treatment in book form. The Nuclear Many-Body Problem is written for students with a basic knowledge of quantum mechanics and some understanding of nuclear phenomena. The book has become a classic for teaching the most funda- mental methods in nuclear physics.