  We present a rigorous formulation of generalized Kohn-Sham density-functional
theory. This provides a straightforward Kohn-Sham description of many-body
systems based not only on particle-density but also on any other observable. We
illustrate the formalism for the case of a particle-density based description
of a nonrelativistic many-electron system. We obtain a simple diagrammatic
expansion of the exchange-correlation functional in terms of Kohn-Sham
single-particle orbitals and energies; develop systematic Kohn-Sham formulation
for one-electron propagators and many-body excitation energies. This work is
ideally suited for practical applications and provides a rigorous basis for a
systematic development of the existing body of first-principles calculations in
a controllable fashion.
