Chapter I considers cyclotron oscillations of an equilibrium plasma (the cyclotron heating problem). It is devoted mainly to the analysis of processes that lead to energy exchange between oscillations and a plasma in cyclotron resonance in an inhomogeneous magnetic field. According to present-day concepts, such an exchange is effected by excitation of modulated beams. The oscillations due to individual beams are analogous to the known Van Kampen waves. In the presence of a thermal spread of the plasma-particle velocity, the interference quenches these oscillations. As a result, the energy drawn by the plasma from the cyclotron wave takes on a thermal (random) form. An appendix (at the end of the article) traces the analogy with Cerenkov resonance in an inhomogeneous plasma and with surface absorption of the oscillations incident on an abrupt plasma boundary (anomalous skin effect). Chapter II summarizes earlier results on the analysis of the stability of a plasma not in thermal equilibrium situated in the inhomogeneous field of a magnetic trap. It was shown in the earlier papers that, depending on the conditions on the plasma boundaries, an increase in the inhomogeneity of the magnetic field can lead to either a lowering of the increment of the unstable natural oscillations (oscillation-reflecting boundaries), or to their total stabilization (absorbing boundaries). Two approaches to the investigation of stability are compared in the review, viz., analysis of the natural oscillations and an investigation of the evolution of the initial perturbations with time.