Dispersive and wave equations form an important class of equations. These include nonlinear equations and the wave maps equation. This introductory text describes the methods and results used ion modern analysis of the Cauchy problem. Working from his lectures at eh NSF-CBMS region conference at New Mexico U. in June 2005, Tao covers ordinary differential equations, constant coefficient linear dispersive equations, semilinear dispersive equations, the Korteweg de Vries equation, energy-critical semilinear dispersive equations and wave maps. Appendices include tools from harmonic analysis and material on the construction of ground states. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)