About two-thirds of all galaxies are spiral galaxies, and a large number of them, more than two-thirds, have a regular spiral structure with two arms that can be followed continuously from the centre of the galaxy (the central bulge) to the extremities of the disc. This structure has for a long time posed a serious theoretical problem concerning its origin and persistence in galaxies. The density-wave theory and the amplification mechanism of these waves provide a beautiful solution to the problem in the majority of cases. Before going into the details of this theory (in Section 5.2), we must first tackle the problem of the gravitational stability of a galactic disc and define the main characteristics of the orbits of stars in a rotating disc (the theory of epicycles).