  A novel approach to the description of superconductors in thermal equilibrium
is developed within a formally exact density-functional framework. The theory
is formulated in terms of three ``densities'': the ordinary electron density,
the superconducting order parameter, and the diagonal of the nuclear N-body
density matrix. The electron density and the order parameter are determined by
Kohn-Sham equations that resemble the Bogoliubov-de Gennes equations. The
nuclear density matrix follows from a Schroedinger equation with an effective
N-body interaction. These equations are coupled to each other via
exchange-correlation potentials which are universal functionals of the three
densities. Approximations of these exchange-correlation functionals are derived
using the diagrammatic techniques of many-body perturbation theory. The bare
Coulomb repulsion between the electrons and the electron-phonon interaction
enter this perturbative treatment on the same footing. In this way, a truly
ab-initio description is achieved which does not contain any empirical
parameters.
