The aim of this article is the representation of the theory of nuclear matter with the technique of many‐body Green functions. We have treated the theory of Green functions thoroughly in the first chapters taking support of the functional method, which offers a convenient approach to the construction of the theory. After treatment of the properties of the exact two‐point function and of the effective single‐particle potential, preconditions and properties of the approximate solutions are discussed. Results achieved todate are treated in chapter 6. Brueckner theory and allied methods are not further discussed, since these are sufficiently known. The theory of linear response, being important for the semi‐phenomenological treatment of real atomic nuclei, is presented in appendix A.