Abstract
Much of the recent work on inverse scattering theory is based on the use of special topics in functional analysis and the theory of Sobolev spaces. The results that we plan to present in this book are no exception. Hence we begin our book by providing a short introduction to the basic ideas of functional analysis and Sobolev spaces that will be needed to understand the material that follows. Since these two topics are the subject matter of numerous books at various levels of difficulty, we can only hope to present the bare rudiments of each of these fields. Nevertheless, armed with the material presented in this chapter, the reader will be well prepared to follow the arguments presented in subsequent chapters of this book.