Inverse problems are a very important area of Physics, other sciences, and applied mathematics. They can be very difficult to tackle, and their proper application is of tremendous value and importance.

This is an immensely well-written, readable, and clear account of various techniques and applications of inverse problems. It is very systematic and elegant in its presentation. The book introduces many important Green-function and eigenfunction techniques and concepts. It would be a major source of information on this field, valuable to graduate students and researchers in many fields of applied and theoretical science. The topics covered include “Radiation and boundary-value problems in the frequency domain,” “Angular-spectrum and multipole expansions,” “Scattering theory,” “Time-reversal imaging for systems of discrete scatterers,” and many others. Each chapter concludes with a detailed guide to further reading materials, as well as a collection of assorted problems of varying levels of difficulty.

Two problems that I have with this book are: it is overly theoretical and it doesn’t have any worked-out examples. Most of the problems at the ends of the chapters are the proof-of-theorem kinds of problems and completion of derivations. Coupled with the almost total lack of detailed derivations or worked-out examples, this book is not the most pedagogically oriented book that I’ve come across. It is probably best suited as a supplementary book in a course with other more practical resources, or as a textbook in a applied mathematics class.