The paper is an introduction to the theory of solid-state masers with particular reference to the travelling-wave maser. The relevant properties of paramagnetic ions are described and the quantum theory of maser action is outlined qualitatively. A semi-classical treatment is developed which is based on the classical equation of motion of a magnetic dipole. It is used to evaluate the engineering characteristics of a travelling-wave maser which employs the comb type of slow-wave guide.