Shelstad will continue her work on twisted endoscopy for reductive groups. This is a part of the theory of automorphic forms which she has been instrumental in developing, and is based on the general representation theory of reductive Lie groups. It is also planned to develop Igusa theory for orbital integrals on real groups. The goal is to obtain results useful for multiplicity formulas for automorphic representations. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.