  The moduli space of the Calabi-Yau three-folds, which play a role as
superstring ground states, exhibits the same {\em special geometry} that is
known from nonlinear sigma models in $N=2$ supergravity theories. We discuss
the symmetry structure of special real, complex and quaternionic spaces. Maps
between these spaces are implemented via dimensional reduction. We analyze the
emergence of {\em extra} and {\em hidden} symmetries. This analysis is then
applied to homogeneous special spaces and the implications for the
classification of homogeneous quaternionic spaces are discussed.
