  The basic mathematical properties of Green's functions used in statistical
mechanics as well as the equations defining these functions and the techniques
of solving these equations are reviewed. An approach is presented called the
Correlated Iteration Theory, which has been developed by the author. This
approach differs from all other known variants of perturbation theory for
Green's functions by the combination of two factors: the systematic formulation
of an algorithm for obtaining subsequent approximations and the consistent
consideration of interparticle correlations at each step of the procedure.
