  We review Migdal's Theory of Finite Fermi Systems and its application to the
structure of nuclei. The theory is an extension of Landau's Theory of
Interacting Fermi Systems. In the first part the basic formulas are derived
within the many body Green functions approach. The theory is applied to
isovector electric giant resonances in medium and heavy mass nuclei. The
parameterizations of the enormalized effective ph-interaction and the effective
operators are discussed. It is shown that the number of free parameters are
restricted due to conservation laws. We also present an extension of Migdal's
theory, where the low-lying phonons are considered in a consistent manner. The
extended theory is again applied to the same isovector electric giant
resonances and to the analysis of $(\alpha,\alpha^\prime)$ reaction data. We
point out that the extended theory is the appropriate frame for self consistent
nuclear structure calculations starting from effective Lagrangians and
Hamiltonians.
