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 themagnetic 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 isimportant 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 ofnumerical simulation. The book should be useful to practitioners of magnetic recording, and to physicists studying magnetic phenomena.