In a monograph based on quasi-classical and quantum descriptions of magnetically ordered media, the physical nature of magnetic solitons is clarified. The idea of ​ ​ them as a connected state of a large number of elementary excitations - magnons is presented. The mathematical theory of solitons in one-, two-and three-dimensional systems is considered, which allows, from a single point of view and within the framework of one model, to consider a wide variety of localized solutions: dynamic and topological solitons, domain boundaries, magnetic vortices, etc.