Theoretical research in elementary particle physics and astrophysics will investigate versions of superstring theory in which the cosmological constant vanishes even though the world predicted by these versions is, as observed, not supersymmetric. Superstring theory is a promising attempt to unify our understanding of all the forces of nature. The cosmological constant, a quantity which could in general occur in the equations which describe the expansion of the universe, is observed to be at most very tiny. This fact has proved very difficult to understand, and the work to be done here is an attempt to help solve the puzzle.