Optimal transportation and applications: lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September 2-8, 2001

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Amp?re and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view.

The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.