Singular curves, Chow Rashevsky theorem. Examples of sub-Riemannian structures. Regularity of natural sub-Riemannian objects such as surveying or distance SR. The theory of optimal transport. Monge and Kantorovich problems and explain how to obtain results of existence and uniqueness of very general optimal transport applications. Monge problem for the cost sub-Riemannian quadratic and links with sub-Riemannian curvature phenomena. Lecture notes will be available.