Encouraged by the friendly reception given to the first edition, I have preserved its basic form and most of the details. The new and revised material occurs mainly in the latter half, on waves. There is one completely new chapter, intended to provide an elementary introduction to the so-called solitary wave, or soliton, which has become such a pervasive feature of physical science. It seemed to me that it should be possible to base an explanation of the solitary wave on the simplest notions of non-linear waves, and chapter 16 is my modest attempt. Consequential changes were necessary in chapter 12, but I believe the outcome is a more helpful treatment of dispersion, even for those who have no immediate need of the solitary wave material. Apart from these and other, smaller, changes, I have added some 30 new problems, the majority of which introduce new physical examples of vibrations and waves.

Most of the work was done during a further period of Study Leave from the University of Liverpool. Of the many people who made valuable comments on the first edition, I am particularly grateful to my Liverpool colleagues Professor J. R. Holt and Dr A. N. James, and their students.

A number of new diagrams were drawn for this edition by Roderick Main.