A review of super riemannian space-time using differential forms

We analyse the content of curved super space-time, which consists of points labelled by four ordinary space-time variables and a set of anti-commuting quantities. A definition of a curved manifold including such variables is given, and a coordinate free formalism reviewed using the super space-time extended version of modern differential geometric techniques. Such a formalism allows the incorporation of internal symmetries in a geometric fashion. Finally we analyse the extended version of Einstein's source-free equation on this manifold, particularly in the linear approximation.