The purpose of this special collection of peer-reviewed papers was to provide an opportunity for scientists from all over the world to share details of recent advances in the physics of magnetic materials.Volume is indexed by Thomson Reuters CPCI-S (WoS).The work is divided into: I. To the Memory of S.V.Vonsovsky, II. Spin-Polarized Transport, III. Spin Dynamics, Spin Waves, Spin-Wave Resonance, IV. Spin Reorientation Phase Transitions, V. Spin-Orbit and Exchange Interactions, Magnetic Anisotropy and Magnetostriction, VI. Dynamics of Domain Structures and Domain Walls, VII. Magnetic Nanostructures and Films, VIII. Magnetism and Nanomaterials, IX. Low-Dimensional Magnetism, X. Magnetism of Strongly Correlated Systems, XI. Magnetotransport and Magneto-Optics.It is expected that this book will become an invaluable source of information on the modern physics of magnetic phenomena and the technology of magnetic materials.The fourth symposium drew scientists from Russia and around the world to share their thoughts and findings about magnets and magnetism. Some 120 papers look at spin polarized transport; spin dynamics, spin waves, and spin-wave resonance; spin reorientation phase transitions; spin-orbit and exchange interactions, magnetic anisotropy, and magneto-restriction; dynamics of domain structures and domain walls; magnetic nanostructure and films; magnetism and nanomaterials; low-dimensional magnetism; the magnetism of strongly correlated systems; magneto-transport and magneto-optics.