This is a text for a two-semester or three-quarter sequence of courses in partial differential equations. It is assumed that the student has a good background in vector calculus and ordinary differential equations and has been introduced to such elementary aspects of partial differential equations as separation of variables, Fourier series, and eigenfunction expansions. Some familiarity is also assumed with the application of complex variable techniques, including conformal map­ ping, integration in the complex plane, and the use of integral transforms. Linear theory is developed in the first half of the book and quasilinear and nonlinear problems are covered in the second half, but the material is presented in a manner that allows flexibility in selecting and ordering topics. For example, it is possible to start with the scalar first-order equation in Chapter 5, to include or delete the nonlinear equation in Chapter 6, and then to move on to the second­ order equations, selecting and omitting topics as dictated by the course. At the University of Washington, the material in Chapters 1-4 is covered during the third quarter of a three-quarter sequence that is part of the required program for first-year graduate students in Applied Mathematics. We offer the material in Chapters 5-8 to more advanced students in a two-quarter sequence.