Algebraic and diagrammatic methods in many fermion theory Introduction Operator algebra The independent particle model Occupation number formalism Diagrams Configuration interaction method Many body perturbation theory The coupled cluster method. This text on the use of electron correlation effects in the description of the electronic structure of atoms molecules and crystals is intended for graduate students in physical chemistry and physics. Modern theories of electronic structure and methods of incorporating electron correlation contributions are developed using a diagrammatic and algebraic formulation and the methods developed in the text are illustrated with examples from molecular and solid state quantum mechanics. A brief Introduction is followed by chapters on operator algebra the independent particle model occupation number formalism and diagrams. Additional topics include the configuration interaction method the many body perturbation theory and the coupled cluster method