abstract: In these lectures I will describe some recent advances in the theory of the nonlinear dispersive equations. The topics to be covered will: recent advances on the well-posedness theory of the Benjamin-Ono equation and the Schrodinger map system, unique continuation results for the Korteweg-De Vriess equation, and blow-up, global existence and scattering for the energy critical Schroedinger and nonlinear wave equations.