The monograph contains a complete and closed statement of the current state of the theory of quasi-one-dimensional magnetic solitons. In addition to the traditional description of the nonlinear dynamics of magnets using the LandauLifshitz equations, the method of phenomenological spin wave Lagrangians is presented. The most effective methods of integrating nonlinear equations - the method of inverse scattering problem and the procedure of "dressing" - are used to construct and analyze soliton solutions of basic models of the theory of magnetism. Landau-Lifshitz equations for isotropic ferromagnets, quadratic magnetizable ferromagnets, two-lattice ferrimagnets, and kyral models for multilattice magnets. Special variants of the reductive perturbation theory are developed to study the weakly nonlinear dynamics of exchange-magnetostatic waves in plates of final thickness, as well as magneto-elastic solitons .. Within the framework of the sine-Gordon model, a highly nonlinear dynamics is analytically described in the spiral structures of magnetists without an inversion center. The book is addressed to researchers, graduate students and students of universities of relevant specialties .