This work addresses the many-electron theory of the solid state. Mastery of the material in it should equip the reader for research in areas such as high-temperature superconductors and the fractional quantum Hall effect. The whole book has been designed to provide the diligent reader with a wide variety of approaches to many-electron theory. The level of the book is suitable for research workers and higher-degree students in a number of disciplines, embracing theoretical physics, materials science and solid-state chemistry. It should be useful not only to theorists in these areas but also to experimental scientists who desire to orient their programmes to address outstanding questions raised by many-body theory.