The quantitative modelling of trace element behaviour in magmatic systems is now one of the key tools employed by petrologists and geochemists in the understanding of the formation and evolution of magmatic rocks and their residues. The approach is all the more meaningful today due to the proliferation of high quality trace element data produced from ICPMS instruments together with more widely available partitioning data and an enhanced understanding of the factors that govern solid–melt partitioning. While many texts on geochemistry or petrology cover aspects of the theory presented here, none covers it as comprehensively, apart from volumes that are collections of research papers in which the information is far less accessible to the junior researcher. To this extent, the book fills a hole in the market.

The text of the book is broken down into relatively short, very readable chapters, nine in all that span 240 pages of text. The list price is £65 hardback, £24 paperback. The text is concise and well written and the equations well presented. Key equations are developed in a logical and systematic manner so that the reader can follow the derivation, rather than merely being presented with the relevant equations to use. The quality of line diagrams is generally adequate although there are a few ‘fuzzy’ reproductions from older texts that would ideally have been drawn again. The quality of reproduction of the photograph of melt distribution in a Norwegian gneiss is poor, especially for a text of this price. Fairly comprehensive references are listed at the end of each chapter.

Chapter 1 is a very welcome and informative introduction to sampling theory and the practical problems of sampling heterogeneous igneous rocks, together with some remarks about data quality. I would have liked to have seen more discussion about how to assess data quality and, ideally, some information of the relative strengths and weaknesses of the different commonly used analytical methods. Chapter 2 includes a brief description of the practicalities of the measurement of partition coefficients and the factors that influence partition coefficients. This part of the text would have benefited from a more extended discussion of the development and details of the lattice strain model but is otherwise a sound treatment.

Chapters 3, 4 and 5 deal in progressively more detail with the behaviour of trace elements during the process of crystallization in progressively more diverse situations. Chapter 6 is a nice summary of the ways in which a researcher can interrogate a given dataset for evidence of the variety of crystallization processes described previously.

Chapters 7 and 8 cover the process of melting, including a discussion of the effects of volatiles, with the usual focus on the melts that are produced but very little discussion about the trace element systematics of the resulting residues. As someone who works on melting residues this is one of my frustrations with almost all texts on this subject and future writers would do well to cater for ‘the other half’! Chapter 9 deals with the more advanced topic of ‘dynamic melting’, where adiabatic melting more directly simulates melting in the real world and factors such as melt percolation are briefly considered. The index is sparse but probably adequate.

Overall this is a very clearly written book that will find extensive use by advanced undergraduates and will act as an excellent reference text for the post-graduate and research community. My feeling is that the book is just a little too concise in most areas, especially given the cost, and the reader is left ‘hanging’ a little in places. Even though the title of the book makes it clear that this is a theoretical treatment I would have liked to have seen more ‘real’ examples so that the reader can evaluate how theory matches reality. Even at the reduced price of the paperback, this book does not represent good value for money – it is clearly mis-priced and this will surely affect its market. This aspect detracts from what is otherwise a valuable contribution.