This volume, together with the next, is intended as the proceedings of expository lectures in Special Months “Nonlinear Dispersive Equations”. Nonlinear dispersive equations, such as nonlinear Schrodinger equations, KdV equation, and Benjamin-Ono equation, are of mathematical and physical importance. Expository courses in August 2004 are intended to cover a broad spectrum of the issues, from mathematical and physical backgrounds to the latest developments.