The monograph presents the results of research in the field of theoretical and computational transonic aerodynamics. In addition to the general issues of transonic theory, the following problems of a fundamental applied nature are considered: transonic vortex current behind the departed shock wave; formation and properties of hanging shock waves; wing profile flow at high subsonic flight speeds, in particular, subcritical wing profiling; profiling the Laval nozzle in the correct setting and the direct task of the nozzle; transonic jet flow; theory of axisymmetric transonic currents; some issues relevant to spatial currents. The book is intended for scientists, students and graduate students specializing in the field of aerogasdynamics.