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Transonic flow has been defined as flow in which regions of subsonic and supersonic flow occur each of significant extent, so that across the common boundaries of these regions fluid particles are accelerated or decelerated through the speed of sound. By the term ‘significant’ is here implied significant for the particular problem or flow characteristic under consideration. Hence for problems in which viscous effects are of major interest the flow past a body at any main stream supersonic speed is strictly speaking transonic in so far as a region of subsonic flow must exist in the bounday layer adjacent to the surface. The book under review is confined, however, to the theory of transonic flow of an inviscid fluid, and the main application of this theory is to problems that arise in considering the flow past wings and bodies at main stream Mach numbers in the range from about 0.8 to 1.2.