  The Green's function formalism in Condensed Matter Physics is reviewed within
the equation of motion approach. Composite operators and their Green's
functions naturally appear as building blocks of generalized perturbative
approaches and require fully self-consistent treatments in order to be properly
handled. It is shown how to unambiguously set the representation of the Hilbert
space by fixing both the unknown parameters, which appear in the linearized
equations of motion and in the spectral weights of non-canonical operators, and
the zero-frequency components of Green's functions in a way that algebra and
symmetries are preserved. To illustrate this procedure some examples are given:
the complete solution of the two-site Hubbard model, the evaluation of spin and
charge correlators for a narrow-band Bloch system, the complete solution of the
three-site Heisenberg model, and a study of the spin dynamics in the
Double-Exchange model.
