  The electronic properties of correlated metals with a strong electron-phonon
coupling may be understood in terms of a combination of Landau's Fermi-liquid
theory and the strong-coupling theory of Migdal and Eliashberg. In these
lecture notes we discuss the microscopic foundations of this phenomenological
Fermi-liquid model of correlated, strong-coupling metals. We formulate the
basic equations of the model, which are quasiclassical transport equations that
describe both equilibrium and non-equilibrium phenomena for the normal and
superconducting states of a metal. Our emphasis is on superconductors close to
equilibrium, for which we derive the general linear response theory. As an
application we calculate the dynamical conductivity of strong-coupling
superconductors.
