When a bed of rigid particles, supported below by a porous plate, is subjected to an increasing upward flow of air, at first nothing happens. Then as the flow increases, the bed can expand slightly and particles can move in relative motion. At higher velocities, large voids (bubbles) can appear which rise like bubbles to the top of the bed, upon which solid objects can float. Such a state is called fluidization and is the subject of this excellent monograph by one of the world's leading figures in the field. Such systems have enormous industrial application in fields as diverse as combustion, pneumatic transport, sedimentation and breakfast cereal manufacture. For some reason physicists have shunned this difficult field for far too many years. This is despite the fact that the behaviour of a particle/fluid system was studied by Einstein, who was the first to show that the effective viscosity for a dilute suspension of rigid spheres is greater than the viscosity of the ambient fluld by a factor of (5/2)α where α is the concentration of particles by volume. Of course, α is very large in fluidized beds but the field is crying out for significant theoretical investment because, even though the modelling of such systems is possible in principle, the forces and couples acting on individual particles present a significant obstacle to progress simply because of the large numbers of particles involved. In fact, no progress can be made without some averaging process and it is here where Jackson writes a marvellous chapter (chapter 2) on the pitfalls that await the unwary. He writes without fear of distinguished authors who have made modelling errors in equations that have even been reproduced by others. He even supplies the missing terms. This chapter alone is worth the price of the book. Jackson achieves his aim by subjecting candidate equations to an analogue of Galileo's `Pisa' experiment. But instead of dropping balls from a tower he imagines dropping the whole fluidized bed. Specifically he imagines a uniform dispersion of particles initially at rest in a fluid also at rest, inside a container, subject only to a uniform gravitational field. If the container is then allowed to fall freely and simultaneously the constraints on the particles are removed, the container and both phases should fall with the acceleration of the gravitational field. This is so simple a test yet too many candidate sets of equations fail this test. The rest of the book relies heavily on theory, with comparison being made with experiment wherever possible. Amongst other highlights is a careful discussion of the nondimensionalization of equations, the necessary empirical closures and careful expositions of existing work on stability of a uniformly fluidized state and the motion of voids. Two final chapters deal with riser and standpipe flows. Overall I enjoyed the book tremendously and learned a lot. Minor quibbles include the lack of discussion of the famous Geldart diagram which, despite being written in dimensional units, still manages to classify the different types of fluidized behaviour. Also missing is a concluding chapter or summary, which could have brought together the different strands of the book. Jackson has written an excellent, challenging account of the subject and has laid bare some uncomfortable truths about the past modelling of such systems. The future of this area is enormously bright for those physicists who can tear themselves away from chasing Nobel prizes and instead follow Einstein into a different field. S J Hogan