This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg-de Vries equation and the nonlinear Schrodinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrodinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrodinger equation and the generalized Korteweg-de Vries equation, properties of their...