A physical and mathematical description of maser oscillator is given with particular emphasis upon explaining the structure of the output line shape. Several approaches to the problem are taken. A qualitative description of the motion of the spin vector is followed by a derivation of the equations pertinent to the interaction of a tuned circuit (microwave cavity) and precessing spins. The resultant equation is nonlinear. Approximate solutions are given and these are plotted as output amplitude vs time. In addition, the equations are solved with numerical solutions for specific experimental conditions by means of a digital computer. The numerical results are compared with experimental data including that taken in our laboratory. The field‐swept oscillator line shapes are explained by the analysis, and the steady state oscillator is described as well.