In this talk, after a short introduction to Courant algebroids and the related algebras defined by them, we will present the notion of Dorfman connection of a Courant algebroid on a vector bundle and some basic results about this. Then, we will present the role of such connections in the attempt of the definition of the Atiyah class of Manin pairs.

This is a joint work with Panagiotis Batakidis.