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accumulated is impressive, but it is not an easy read. Readers familiar with Stefan problems will almost certainly find their favourite approaches detailed here, but anybody new to the field will miss being led through the foothills in order to find the approach most suited to them, and to navigate past methods that may not apply to their particular problem. The approach is concise and mathematical: and here a note on terminology is appropriate. The term ‘classical’ is often used to denote the problem in which temperature is continuous, but this book also discusses weak or generalised solutions which allow discontinuities. The first three chapters introduce the problem, set it in its thermodynamical and metallurgical context, and consider the multiphase problem. Then supercooling, superheating and volumetric heat sources, and the steady-state problems are discussed. After a chapter on variational inequalities for elliptical and parabolic systems formulation of the problem with a hyperbolic rather than parabolic heat transfer model is presented. After a very useful discussion of the inverse Stefan problem, the original book finished with some analysis of the classical solutions and of the regularity of some weak solutions. The bulky chapter on quasi-analytical solutions that has been added to this edition ranges over exact analytical solutions, solutions in series, analytical-numerical solutions of both the Stefan problem and its inverse. Hyperbolic problems, conformal mapping, and approximate methods including perturbation are also covered. Unfortunately something has gone badly wrong with the type-setting of the bibliography: almost every entry has one or more spurious characters. It is surprising that this should have slipped through proof-reading. There are a few other minor inconsistencies or typographical slips (for example, ∇f is defined as the gradient of f in the list of symbols, whereas grad f is often used in the text), but these should not cause major problems. As an up-to-date reference work for the experienced practitioner, this is a valuable addition to the library. Beginners, however, should look elsewhere.