Lie algebroids from the point of view of noncommutative geometry

I will introduce the notion of a Lie algebroid and explain how they can be viewed as generalizations of both tangent bundles and Lie algebras. The first point of view, as a generalized tangent bundle, leads to a de Rham type differential calculus. The second point of view, as generalized symmetries of the underlying manifold, opens the way to noncommutative geometry via the universal enveloping algebra of the Lie algebroid. The aim of this talk, based on joint work with Arie Blom, is to compare these two approaches using Hochschild and cyclic homology.