The first Nato Advanced Studies Institute entirely devoted to density functional theory was held in Portugal in September 1983. The proceedings of this School, publis hed in early 1985, is still used as a standard reference covering the basic development of the theory and applications in atomic, molecular, solid state and nuclear physics. Ho wever, astonishing progress has been achieved in the intervening years: The foundations of the theory have been extended to cover excited states and time dependent problems more fully, density functional theory of classical liquids and superconducting systems has been addressed and extensions to relativistic, that is, field theoretical systems, as well as a more thorough discussion of magnetic field problems have been presented. In addition, new functionals have been devised, for instance under the heading of ge neralised gradient expansions, and the number of applications in the traditional fields has steadily increased, in particular in chemistry. Applications in new fields, as for instance the structure of atomic clusters and the marriage of density functional theory with molecular dynamics and simulated annealing, have provided additional impetus to the field of density functional theory."

The year 2004 was a remarkable one for the growing ?eld of time-dependent density functional theory (TDDFT). Not only did we celebrate the 40th - niversary of the Hohenberg-Kohn paper, which had laid the foundation for ground-state density functional theory (DFT), but it was also the 20th - niversary of the work by Runge and Gross, establishing a ?rm footing for the time-dependent theory. Because the ?eld has grown to such prominence, and has spread to so many areas of science (from materials to biochemistry), we feel that a volume dedicated to TDDFT is most timely. TDDFT is based on a set of ideas and theorems quite distinct from those governingground-stateDFT, butemployingsimilar techniques.Itisfarmore than just applying ground-state DFT to time-dependent problems, as it - volves its own exact theorems and new and di?erent density functionals. Presently, themostpopularapplicationistheextractionofelectronicexcit- state properties, especially transition frequencies. By applying TDDFT after thegroundstateofamoleculehasbeenfound, wecanexploreandunderstand the complexity of its spectrum, thus providing much more information about the species. TDDFT has a especially strong impact in the photochemistry of biological molecules, where the molecules are too large to be handled by t- ditional quantum chemical methods, and are too complex to be understood with simple empirical frontier orbital theo