  A Chern-Weil construction for extensions of Lie-Rinehart algebras is
introduced. This generalizes the classical Chern-Weil construction in
differential geometry and yields characteristic classes for arbitrary
extensions of Lie-Rinehart algebras. Some examples arising from spaces with
singularities and from foliations are given that cannot be treated by means of
the classical Chern-Weil construction.
