This book has three parts, each of about 250 pages; so it covers a lot of material, and is certainly good value. It is suitable as the main text for a masters degree in physics. The author has tried to steer a middle course between the gory technical details of quantum field theory, and a merely impressionistic outline in which no technique is needed and none is acquired. Another aim was to select and at least mention the main lines of current theories of elementary particles. He has succeeded quite well on both counts.

It is pleasing to see quantum field theory again placed centre stage; the prototype, quantum electrodynamics, is treated in the first part, and in enough detail to offer an account of the derivation of the anomalous magnetic moment of the electron, and of the Lamb shift. These are the two great predictions of QED, and their verification to eight or nine significant figures by experiment shows that the theory is certainly nearly right.

In brief but adequate style, Part II covers Feynman path integrals, nonabelian gauge theory and the "standard model". This is, at present, the best candidate as the theory of fundamental particles without gravity. An essential part, the Glashow-Salam-Weinberg theory of weak interactions, won the inventors the Nobel prize in 1979. To an outsider, the theory seems to be strewn with whimsical jargon: quarks, anomalies, asymptotic freedom, infrared slavery, skeletons, ghosts, charm, technicolour, exotics, Gut theory, and everything the author knows, and much much more. The theory is compared to the experimental facts on fundamental particles, and some prior knowledge of this subject would help.

Part III is even harder; it aims at the inclusion of gravity within the quantum theory of particles. There is a serious attempt at providing the reader with all the necessary background for this. There is a 30-page chapter on statistical mechanics, one on lattice gauge theory, and another on solitons, monopoles and instantons. Two (now abandoned) earlier theories of quantum gravity are given in outline. Each chapter is a survey of the lifetime's work of dozens of people. The text is geared to culminate in the triumphant last 50 pages, which describe the superstring; this is optimistically claimed to be the final, ultimate theory.

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While the author is generally successful in his attempt to select teachable material, and is able to illustrate theoretical points by simple, realistic cases, the text is not a mathematical treatise, such as "The Theory of Sound", by Rayleigh. Sometimes useful techniques are introduced as new axioms, when they could actually be derived from what went before. Examples of this style are the axiomatic treatment of the Feynman path integral, and dispersion relations. He thus avoids all mention of a large body of mathematical physics devoted to justifying these concepts.

No mention is made of the rigorous proof of the existence of quantum fields, nor of the triviality of one of his favourite models, ?4. He places his faith in the "Higgs mechanism" even though it is known to be very dubious. The Coleman-Mandula theorem is mentioned five times, but no remotely clear statement of it is given.

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Some of the potted history of science, which leads into each chapter, is repeated from other texts, but the author seems to have invented one story by himself: he says that Schrodinger rejected the Klein-Gordon equation because it gave rise to negative probabilities. This cannot be true, since the probabilistic interpretation only came later, in July 1926. It is true that Schrodinger's notebooks of January 1926 contain the Klein-Gordon equation; it is likely that he could not solve it at that time. But he did solve it for the energy levels in June 1926, and indeed published it. (See F. Hund, The History of Quantum Theory, 1974, p.197.) R. F. Streater is professor of applied mathematics, King's College, London.