The purpose of this book is to provide a detailed description of Brillouin-Wigner methods and their application to the many-body problem in atomic and molecular physics and quantum chemistry. Recently there has been a renewal of interest in Brillouin-Wigner methods. This interest is fuelled by the need to develop robust, yet efficient multireference theoretical approaches to the electron correlation problem together with associated algorithms. Such theories are an essential ingredient of the quantum mechanical description of most dissociative processes in molecules, of excited states, and of ionization and electron attachment processes.