  Riemann surfaces are two-dimensional manifolds with a conformal class of
metrics. It is well known that the harmonic action functional and harmonic maps
are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces
are an analogue of Riemann surfaces in the world of super geometry. After a
short introduction to super differential geometry we will compare Riemann
surfaces and super Riemann surfaces. We will see that super Riemann surfaces
can be viewed as Riemann surfaces with an additional field, the gravitino. An
extension of the harmonic action functional to super Riemann surfaces is
presented and applications to the moduli space of super Riemann surfaces are
considered.

Differential Geometry