This book is not meant to be read sequentially. The material is organized according to a modular structure with abundant cross-referencing and indexing to permit a variety of pathways through it.

Each chapter in Part I, Applications, is devoted to a particular technique: Fourier series, Fourier transform, etc. The chapters open with a section summarizing very briefly the basic relations and proceeds directly to show on a variety of examples how they are applied and how they “work.”

A fairly detailed exposition of the essential background of the various techniques is given in the chapters of Part II, Essential Tools. Other chapters here describe general concepts (e.g., Green's functions and analytic functions) that occur repeatedly elsewhere. The last chapter on matrices and finite-dimensional linear spaces is included mostly to introduce Part III, Some Advanced Tools. Here the general theory of linear spaces, generalized functions and linear operators provides a unified foundation to the various techniques of Parts I and II.

The book starts with some general remarks and introductory material in Part 0. Here the first chapter summarizes the basic equations of classical field theory to establish a connection between specific physical problems and the many examples of Part I in which, by and large, no explicit reference to physics is made. The last section of this chapter provides a very elementary introduction to the basic idea of eigenfunction expansion.