The importance of electron correlation effects for the accurate description of the electronic structure of atoms, molecules and crystals is now widely recognized. In this text, modern theories of electronic structure and methods of incorporating electron correlation contributions are developed using a diagrammatic and algebraic formulation. This approach is intended to facilitate an understanding of the interconnections between the different approaches. As a further aid to understanding, the methods developed in the text are illustrated with examples from molecular and solid state quantum mechanics. The techniques presented here treat such topics as operator algebra, Hartree-perturbation theory and the coupled cluster method. The text is intended for graduate students in physical chemistry and physics.