This classic monograph on unsteady transonic flow — the flow of air encountered at speeds at or near the speed of sound — is of continuing interest to students and professionals in aerodynamics, fluid dynamics, and other areas of applied mathematics. After a brief Introduction, Swedish physicist Mårten T. Landahl presents a chapter in which the two-dimensional solution is derived, succeeded by a discussion of its relation to the subsonic and supersonic solutions. Three chapters on low aspect ratio configurations follow, covering triangular wings and similar planforms with curved leading edges, rectangular wings, and cropped delta wings, and low aspect ratio wing-body combinations. The treatment concludes with a consideration of the experimental determination of air forces on oscillating wings at transonic speeds.