The linear theory of plasma waves in homogeneous plasma isarguably the most mature and best understood branch of plasma physics. Given the recently revised version of Stix's excellent Waves inPlasmas (1992), one might ask whether another book on this subject is necessary only a few years later. The answer lies in the scope of thisvolume; it is somewhat more detailed in certain topics than, and complementary in manyfusion research relevant areas to, Stix's book. (I am restricting thesecomments to the homogeneous plasma theory only, since the authorpromises a second volume on wave propagation in inhomogeneous plasmas.) This book is also much more of a theorist's approach to waves inplasmas, with the aim of developing the subject within the logicalframework of kinetic theory. This may indeed be pleasing to the expertand to the specialist, but may be too difficult to the graduate studentas an `introduction' to the subject (which the author explicitlystates in the Preface). On the other hand, it may be entirelyappropriate for a second course on plasma waves, after the student hasmastered fluid theory and an introductory kinetic treatment of waves ina hot magnetized `Vlasov' plasma. For teaching purposes, my personalpreference is to review the cold plasma wave treatment using theunified Stix formalism and notation (which the author wisely adopts inthe present book, but only in Chapter 5). Such an approach allows oneto deal with CMA diagrams early on, as well as to provide a framework todiscuss electromagnetic wave propagation and accessibility ininhomogeneous plasmas (for which the cold plasma wave treatment isperfectly adequate). Such an approach does lack some of the rigour,however, that the author achieves with the present approach. As theauthor correctly shows, the fluid theory treatment of waves followslogically from kinetic theory in the cold plasma limit. I onlyquestion the pedagogical value of this approach. Otherwise, I welcomethis addition to the literature, for it gives the teacher of thesubject a valuable reference where the inquisitive student will be ableto read up on and satisfy himself about the practicality andreliability of the Vlasov theory in a hot magnetized and collisionlessplasma. The book has excellent treatments of several new topics notincluded in previous textbooks, for example, the relativistic theory ofplasma wave propagation, so important in electron cyclotron heating ofmagnetically confined fusion plasmas, a discussion of current drivetheory and there is a welcome introduction to parametric instabilitiesin the final chapter.There are some things that make the readability of the booksomewhat difficult. In the early parts, certain advancedconcepts are introduced without much motivation or explanation,although the author is trying to be helpful by providing a list ofrelevant references at the end of each chapter. Here the teacher'srole will be critical. Again, a certain amount of previous knowledgeof the subject would prove to be invaluable to thestudent.The main content of the book is included in 11 chapters. Use is made of CGS Gaussian units, a favourite of plasma theorists. As theauthor states, these are still widely used in advanced plasma theory, andthe student is well advised to become familiar with this system ofunits (as well as the SI system for applications). To help the readerin the Introduction, the author defines various expressions often usedin plasma physics in practical units (frequencies in hertz, lengths in centimetres, temperatures in kiloelectronvolts and magnetic fields in teslas). Chapter 2 is entitled `Plasma Electrodynamics' and it introduces the Maxwell-Vlasov set ofequations, as well as the important fundamentals of wave propagation, such as polarization, dispersion and the dielectric tensor, and energyrelations. In Chapter 3, `Elementary Plasma Kinetic Theory', theauthor derives the Vlasov equation and the Fokker-Planck equation fromthe BBGKY hierarchy. This is a somewhat unusual chapter in a book onplasma waves, but I welcome it since it demonstrates the author'sdesire to be complete and rigorous in justifying the use of thecollisionless Vlasov equation for `high frequency' wave propagationphenomena. Incidentally, it is interesting that while the author derivesthe Fokker-Planck equation at great length, it is used only to derivethe fluid and MHD equations, but not for estimating Coulomb collisionaldamping of specific waves in laterchapters.Chapter 4 gives the derivation of the hot plasmadielectric tensor. There is an extensive and excellent discussion ofthe relativistic formulation of the dielectric tensor, which is offundamental importance to practising fusion physicists (for example)involved in ECR heating of high temperature plasmas. Various temperature limits are taken in Chapters 5, 6 and 7, and the author discusses the infinite number of waves in the cold plasma limit (Chapter 5), in the hot plasma limit (Chapter 6) and in the electrostatic limit (Chapter 7). In my opinion, these chapters represent the `meat' of the book. Chapter 7 includes a detailedtreatment of electrostatic waves in a hot plasma, including Bernsteinwaves and their damping at high harmonics. This is a difficult topic, and the extensive treatment presented here is hard to find in othertexts. The author also includes a discussion of two streaminstabilities here, together with the Nyquist-Penrose criterion forinstability.Chapter 8 discusses linear wave-particle interactions,including damping of electromagnetic waves, RF current drive and RFheating. Chapter 9 is called `Collisionless Stochasticity' and institutes an introduction to the subject as well as applicationsto the heating of ions by high harmonic, lower hybrid waves. Chapter 10 isanother key part of the book, on the quasilinear theory of heating andcurrent drive. It deals with the practical aspects of RF heating andcurrent drive in magnetically confined fusion plasmas, and is a `mustread' for researchers dealing with RF heating and related transport. Chapter 11 attempts to deal with non-linear effects in the presence ofhigh power RF waves in plasmas. First, the author deals with thedifficult subject of mode coupling theory, but, owing to its complexity,the formulation is never reduced to practical applications. Only the`dipole approximation' section can be used to make practical estimatesof non-linear effects during RF heating.There are some shortcomings of this book that need to bementioned here. There are some typographical errors, including spelling errors. The labelling on thefigures is often hard to read due to their poor quality and smallsize. The figures themselves are often too small and are overloadedwith curves (e.g., Figs 18.1, 18.2, 21.3, 28.13). The authormust have spent a significant effort in producing these curves, andthey deserve a better presentation, especially if they are to be used bystudents. Ease of readability is important for a textbook intended forstudents and researchers alike. It is hoped that such shortcomingswill be improved in future editions, as well as in Volume II, which is tofollow.To summarize, this book presents an up to date majorcontribution to the field of plasma waves and is a `must' on the shelvesof active researchers as well as advanced graduate students. Under theguidance of a knowledgeable teacher, the book may be used as a text,with appropriate omissions of certain sections for a one semestercourse in plasma waves. Alternatively for those who have mastered thefundamentals of wave propagation in plasmas, the book could be used asa basis for an advanced seminar course.I am looking forward with anticipation to Volume II, Waves in Inhomogeneous Plasmas, by Marco Brambilla, one of the eminent plasma wave theorists of ourgeneration.