  The underlying even manifold of a super Riemann surface is a Riemann surface
with a spinor valued differential form called gravitino. Consequently
infinitesimal deformations of super Riemann surfaces are certain infinitesimal
deformations of the Riemann surface and the gravitino. Furthermore the action
functional of non-linear super symmetric sigma models, the action functional
underlying string theory, can be obtained from a geometric action functional on
super Riemann surfaces. All invariances of the super symmetric action
functional are explained in super geometric terms and the action functional is
a functional on the moduli space of super Riemann surfaces.
