This book is based on a course offered at the California Institute of Technology. Typically, the majority of the students are advanced undergraduates (juniors and seniors), the others being beginning graduate students (mostly engineering). With a class having a firm grasp of advanced calculus, it has been found possible to cover the material, with some omissions in the last two chapters, in a one-quarter course meeting three times a week. Without omissions, and at a somewhat more leisurely pace, the material presented in the book should be sufficient for a one-semester course.