The constrained search approach, mappings to external potentials, and virial-like theorems for electron-density and one-matrix energy-functional theories -- Density matrices, reduced density matrices, a geometric investigation of their properties, and applications to density functional theory -- Properties of one-matrix energy functionals -- Self-interaction correction -- Some recent developments in density functional theory -- Electron gas models and density functional theory -- Electron structure calculations for heavy atoms: A local density approach -- Density functionals obtained from models of the electron first and second order density matrices -- Free energy density functionals for non-uniform classical fluids.