I decided to write this book when I began looking for a textbook for a methods of applied mathematics course that I was to teach during the 1981-1982 academic year. There were many fine textbooks available-with some of the recent ones having been written by friends and colleagues for whom I have a great deal of respect. However, I felt that over the fifteen years that had elapsed since I left the Courant Institute, my research and point of view about the problems of interest to me had evolved in a manner unique to the combination of scientific experiences that have made up my career to date. It was my own point of view that I wanted to communicate in the course I was to teach. Certainly, the reader will find common ground here with other texts and references. However, it is my hope that I have communicated enough of the ideas that comprise my approach to direct and inverse scattering problems to have made this project worthwhile.