  A global analysis of duality transformations is presented. It is shown that
duality between quantum field theories exists only when the geometrical
structure of the quantum configuration spaces of the theories comply with
certain precise conditions. Applications to S-dual actions and to T duality of
string theories and D-branes are briefly discussed.It is shown that a new
topological term in the dual open string actions is required. We also study an
extension of the procedure to construct duality maps among abelian gauge
theories to the non abelian case.
