On the Functional Equations Satisfied by Eisenstein Series Introduction Statement of assumptions. Some properties of discrete groups satisfying the assumptions Definition of a cusp form (after Gelfand). Basic properties of cusp forms Definition of Eisenstein series. Investigation of the constant term in the Fourier expansion of an Eisenstein series. A variant of a formula of Selberg Some lemmas used in Sections 6 and 7 Proof of the function equations for the Eisenstein series associated to cusp forms Proof of the functional equations for all Eisenstein series. Statement of theorem References Appendices.