  This set of lectures contain a brief review of some basic supersymmetry and
its representations, with emphasis on superspace and superfields. Starting from
the Poincar\'e group, the supersymmetric extensions allowed by the
Coleman-Mandula theorem and its generalisation to superalgebras, the Haag,
Lopuszanski and Sohnius theorem, are discussed. Minkowski space is introduced
as a quotient space and Superspace is presented as a direct generalization of
this. The focus is then shifted from a general presentation to the relation
between supersymmetry and complex geometry as manifested in the possible target
space geometries for N=1 and N=2 supersymmetric nonlinear sigma models in four
dimensions. Gauging of isometries in nonlinear sigma models is discussed for
these cases, and the quotient construction is described.
