http://www.math.ias.edu/sp/gpde   In these lectures we will describe the relationship between optimal transportation and nonlinear elliptic PDE of Monge-Ampere type, focusing on recent advances in characterizing costs and domains for which the Monge-Kantorovich problem has smooth diffeomorphism solutions. Background references. L.C Evans, PDE and Monge-Kantorovich mass transfer. Current developments in Mathematics, 1997. Int. Press, Boston, (1999). R. T . Rachev and L. Ruschendorf, Mass transportation problems, Springer,1998. J. Urbas, Mass transfer problems, Lecture Notes, Univ. of Bonn, 1998. C. Villani, Topics in optimal transportation, Amer. Math. Soc. 2003.