It has been said that ‘a true scholar publishes only one book in his lifetime and that posthumously’ [105, p. 435]. In fact, this book has not taken a lifetime to complete, although it has had a very long gestation period: there have been many distractions, most of which have not been unpleasant.

The book is concerned with the scattering of time-harmonic waves by obstacles; the words ‘multiple scattering’ in the title signify that there are at least two obstacles. The problems considered come from acoustics (sound waves, Helmholtz equation), electromagnetics (Maxwell's equations), elastodynamics (waves in solids) and hydrodynamics (surface water waves). The book describes a variety of mathematical techniques for solving such problems: the main techniques involve separation of variables, integral equations and T-matrices. Most of the book is concerned with exact methods, although the last chapter discusses several effective approximate methods. There are also two chapters on addition theorems; these are useful in other contexts as well as for multiple scattering. For detailed information on the topics covered, see the Table of Contents and Section 1.7; for a list of topics not covered, see Section 1.2.

The mathematics used is classical: separation of variables, special functions, Green's functions, Fourier methods, asymptotics. The reader should also have some familiarity with simple uses of boundary integral equations. Operator notation is used when convenient.

As far as I know, there is no other book that treats all four of the main physical domains: acoustics, electromagnetics, elastodynamics and hydrodynamics.