To a beginner in plasma physics the subject of waves can be bewildering, with a seeming myriad of different wave modes and ways of approaching them though cold plasma equations, warm plasma equations or kinetic equations. Add to this the intricacies of Landau and cyclotron damping and the fact that real plasmas are rarely uniform and infinite in extent, even as a first approximation, and the need for a reliable guide through the maze becomes apparent.This is a revised and extended version of a book which has already proved its value as an advanced text at postgraduate level. It contains a careful account of many of the properties of waves using the various possible levels of approach, and a good selection of graphs and surface plots which are a great help to the reader in visualising the behaviour of wave dispersion relations. As might be expected by anyone familiar with the author's research, there is an extensive discussion of waves in an inhomogeneous plasma and the phenomenon of mode conversion which plays a vital role in various plasma heating schemes using waves. Various aspects of the nonlinear theory of waves are discussed, including quasilinear theory, solitons, particle trapping and parametric instability.The discussion throughout is characterised by a clear treatment of both the mathematical problems involved and the underlying physics, the second edition having provided an opportunity for refinement and clarification of the earlier presentation, as well as the addition of new material on recent advances in the subject. Any student who masters the material in this book and works through the problems it contains will have a very solid grounding in the theory of wave propagation. Research workers in the field will find it to be a comprehensive source of information on waves, including a number of topics which have only been found in research papers until now. I think that this is a very welcome addition to the literature which will be a valuable resource for teachers and researchers. Most people with a serious interest in plasma waves will probably think of the work by Stix (Stix T H 1992 Waves in Plasmas (New York: American Institute of Physics)) and its earlier edition as having been the standard work on plasma waves for many years and will wonder how this book compares. The answer is, I think, that the two works complement each other well. Where they overlap the discussion is generally somewhat different and can yield different insights, and each contains material absent from the other. Swanson's book is certainly worth a place beside Stix on the bookshelves of anyone who needs to know about plasma waves.R A Cairns