Electrons in solids behave like microscopic bar magnets, and in certain solids these align to produce macroscopic magnetizations. This book deals with the dynamics of this magnetization field. It addresses questions of microscopic mechanism only to the extent that residual interactions of the magnetic moments with other degrees of freedom of the host solid affect the dynamics, particularly the dissipative aspects. Several of these damping mechanisms are evaluated here for their effect on the equations of the magnetization dynamics. This dynamics is intrinsically nonlinear. This is important in the applications, particularly magnetic recording, which involves very large motion of the magnetization, well beyond the validity of linearized (small motion) approximations or limited extensions thereof. Therefore nonlinear solution methods are emphasized, but with only minimal use of numerical simulation. The book should be useful to practitioners of magnetic recording, and to physicists studying magnetic phenomena. * Broad readership accross condensed matter physics, electrical and materials engineering. * Unique up-to-date reference. * Active topic, of interest to academia and industry. * Will settle some controversies on the form of the dissipative terms in the equations of motion of magnetization fields. * Will stress the possibility of going beyond linearized theory in a number of directions. * Will shed new light on the theory of magnetization reversal, replacing the piecemeal approach currently in use.