The theory of supergravity in (2+1) dimensions, both with and without a cosmological term, is presented. In the latter case, we discover a manifold that has torsion but no curvature. We make extensive use of differential forms and the dimensionality of our space–time allows us to use SL(2,R) spinors. Our results enable us to discuss in an accompanying paper an action describing the theory of a spinning membrane.