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.