The introduction presents a general discussion of electron cyclotron masers (ECM): resonance, relativistic effects, elementary quantum aspects, the classical relativistic bunching and the optimum value of the electric field. The practical structure - in particular that of the gyrotron - is specified only insofar as it is useful for understanding the following chapters. The main parameters are discussed. Section 2 develops a nonlinear adiabatic or orbital theory of electron motion which alleviates calculations considerably while keeping numerical errors low enough for many practical cases. Its results are compared to a rigorous integration in one case. Other cases show the importance of the electric field profile inside the resonant cavity. Section 3 is devoted to space charge phenomena, and, for the most part, to a linear theory with space charge. In its limited range of validity (low-energy electrons), the theory indicates a strong impact of space charge for low a.c. fields and exhibits a pure beam instability. Section 4 is devoted to circuit equations with emphasis on the special features of cavities consisting of a long waveguide near cutoff. The conclusion indicates some trends of gyrotron development and corresponding theoretical problems.