  A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon
equation is performed. Two different forms of the supersymmetric system are
considered. We begin by studying a system of partial differential equations
corresponding to the coefficients of the various powers of the anticommuting
independent variables. Next, we consider the super-sine-Gordon equation
expressed in terms of a bosonic superfield involving anticommuting independent
variables.
  In each case, a Lie (super)algebra of symmetries is determined and a
classification of all subgroups having generic orbits of codimension 1 in the
space of independent variables is performed. The method of symmetry reduction
is systematically applied in order to derive invariant solutions of the
supersymmetric model. Several types of algebraic, hyperbolic and doubly
periodic solutions are obtained in explicit form.
