Compressibility is a property inherent in any material, but it does not always manifest itself. Experience suggests that it affects the medium motion only at velocities comparable to the speed of sound. Why do we study compressibility? It turns out that in order to calculate the aircraft streamlining or the internal flow in its engine, or the shell muzzle velocity, or the dynamic load of a shock wave from an accidental blast on a structural element, and in many other cases it is necessary to know and understand the laws of the Dynamics of Compressible Media (DCM) and be able to apply them in practice. This textbook is designed to help readers achieve this goal and learn the basics of DCM. This field of knowledge is high-tech and always focuses on the future: modern developments of hypersonic aircraft, designing more advanced structural elements for airplanes and helicopters, calculating the car aerodynamics, etc. Paradoxes have always given impetus to the search for new technological devices. Unusual effects in DCM include the flow chocking in supersonic outflow from reservoirs (Sect.2.2); the shock wave formation inside an initially smooth flow (Sect.5.3); the generation of a "spallation saucer" of armor inside a tank when a shell hits it (Sect.5.5); the dog-leg of a plane discontinuity surface at shockwave reflection from a rigid wall (Sec.8.1). The way to understand these and other effects is through the creation of quantitative models of a moving compressible fluid.