Traditionally, density-functional theory (DFT) has been a theory of the ground state of a multi-electronic system. Although excited states were of concern since the beginning of DFT history, realistic calculational schemes have evolved only recently. The reason is that the techniques of ground-state DFT are not suitable enough for an adequate description of excited states. However, there are recent approaches to excited-state DFT that have turned out to be very promising in this notoriously difficult area The object is to find accurate approximations to excited-state energies and densities. In this dissertation several main approaches of modern excited-state DFT are reviewed, certain interrelation between them are revealed, and several new results announced Two universal functionals F1r and F1r are defined. By the use of constraint-search, the following property is proven: E0v
