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This chapter deals with one-dimensional stationary and nonstationary as well as planar and three-dimensional stationary gas flows. The theories for the Laval nozzle and normal and oblique shock waves are presented. The Becker’s solution for the shock wave structure is given. The solution of a simple wave type is obtained with the aid of the method of characteristics. The onset of a gradient catastrophe as well as discontinuous solutions in continuous flows is shown. These effects are caused by the nonlinear terms in the gas dynamics equations. The Chaplygin’s method for the transformation of the solution of stationary gas dynamics equations to the plane of the hodograph variables is presented in detail. A new method is presented for the aerodynamic design of three-dimensional solutions with the aid of the solutions of a lesser dimension.