I have tried to make this book accessible to the average senior undergraduate or beginning postgraduate student in physics, irrespective of specialization. The mathematics used above and beyond what every physics undergraduate is taught is provided in the Mathematical appendices.

A very good idea of the contents of the book may be formed by reading the Prologue and the Introductions to Parts I and II, in that order. They are written, as far as possible, in plain English. They will also give the reader an idea of the mathematics he or she may be lacking.

A firm grasp of sets and mappings and of the mathematical structure of the real number system is basic to the whole book. Appendices A1 and A2 develop this material in sufficient detail. Part I requires an equally firm grasp of basic point-set topology, which is provided in Appendix A3. Completions, both metric and uniform, are treated in Appendix A4. Differentiable manifolds are defined in Appendix A8. There are no exercises so-called, but every now and then the reader is invited to satisfy himself or herself of some point or the other. They should not impose undue hardship, and may usefully be taken up.

Chapters 6–11 of Part II use von Neumann's definition of a separable Hilbert space over the complex numbers, and the basic results of the structure theory of self-adjoint operators, known as spectral theory, on it.