A Lie algebroid over a manifold is a vector bundle over that manifold whose
properties are very similar to those of a tangent bundle. Its dual bundle has
properties very similar to those of a cotangent bundle: in the graded algebra
of sections of its external powers, one can define an operator similar to the
exterior derivative. We present in this paper the theory of Lie derivatives,
Schouten-Nijenhuis brackets and exterior derivatives in the general setting of
a Lie algebroid, its dual bundle and their exterior powers. All the results
(which, for their most part, are already known) are given with detailed proofs.
In the final sections, the results are applied to Poisson manifolds.Comment: 46 page