  A noncommutative gauge theory is associated to every Abelian gauge theory on
a Poisson manifold. The semi-classical and full quantum version of the map from
the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten
map) is given explicitly to all orders for any Poisson manifold in the Abelian
case. In the quantum case the construction is based on Kontsevich's formality
theorem.
