  We develop a systematic framework for studying target space duality at the
classical level. We show that target space duality between manifolds M and
Mtilde arises because of the existence of a very special symplectic manifold.
This manifold locally looks like M x Mtilde and admits a double fibration. We
analyze the local geometric requirements necessary for target space duality and
prove that both manifolds must admit flat orthogonal connections. We show how
abelian duality, nonabelian duality and Poisson-Lie duality are all special
cases of a more general framework. As an example we exhibit new (nonlinear)
dualities in the case M = Mtilde = R^n.
