  We introduce and discuss (local) symmetries of geometric structures. These
symmetries generalize the classical (locally) symmetric spaces to various other
geometries. Our main tools are homogeneous Cartan geometries and their explicit
description. This allows us to describe the structure of symmetric geometric
structures and to provide a general construction of such structures. Since we
can view the classical (locally) symmetric spaces as special case, this allows
us to classify various geometric structures on semisimple symmetric spaces.
Then we investigate the case of symmetric parabolic geometries in detail and
obtain classification of symmetric AHS-structures and symmetric parabolic
contact geometries in the semisimple cases.
