  A simple geometric description of T-duality is given by identifying the
cotangent bundles of the original and the dual manifold. Strings propagate
naturally in the cotangent bundle and the original and the dual string phase
spaces are obtained by different projections. Buscher's transformation follows
readily and it is literally projective. As an application of the formalism, we
prove that the duality is a symplectomorphism of the string phase spaces.
