An account is given of the mathematical theory of the motion of a rocket in flight. The aerodynamic forces and couples, and those due to the action of the burning gases, are investigated as fully as possible, and the equations of motion are set up in their most general form. The effects of a variety of disturbing factors, such as wind and asymmetries of design and functioning, are considered. Solutions of the equations, most of which are suitable for numerical computation, are given under various assumptions regarding the form of the axial spin, the aerodynamic lift moment, the acceleration, etc. A thorough investigation of the conditions necessary for stable motion is carried out. The paper concludes with a summary in which the main features of rocket motion, as revealed by the theory, are discussed in general terms