From a complex analytic perspective Teichmüller space - the universal
cover of the moduli space of Riemann surfaces - is a contractible
bounded domain in a complex vector space. Likewise, Bounded Symmetric
domains arise as the universal covers of locally symmetric varieties
(of non-compact type). In this talk we will study isometric maps
between these two important classes of bounded domains equipped with
their intrinsic Kobayashi metric.