SOME RELATIONSHIPS BETWEEN DUALITIES IN STRING THEORY

Some relationships between string theories and eleven-dimensional supe rgravity are discussed and reviewed. We see how some relationships can be derived from others. The cases of N = 2 supersymmetry in nine dime nsions and N = 4 supersymmetry in four dimensions are discussed in som e detail. The latter case leads to consideration of quotients of a K3 surface times a torus and to a possible peculiar relationship between eleven-dimensional supergravity and the heterotic strings in ten dimen sions.