  We develop the global moduli theory of symplectic varieties in the sense of
Beauville. We prove a number of analogs of classical results from the smooth
case, including a global Torelli theorem. In particular, this yields a new
proof of Verbitsky's global Torelli theorem in the smooth case (assuming
$b_2\geq 5$) which does not use the existence of a hyperk\"ahler metric or
twistor deformations.
