In this book, the authors gather and present recent advances in magnetism research. Topics discussed include the field theory of magnetism; long-range order (LRO) and phase transition in the quantum anisotropic ferromagnetic Ising-Heisenberg linear chain; Green's function method in the Bogoliubov-Tyablikov version of the quantum theory of magnetism; diluted magnetic semiconductors; perpendicular magnetic anisotropy in half-metallic Heusler alloy films; a comparative study of the structural and physical properties of spinel nano-ferrites synthesized by a co-precipitation method; and the hysteretic behavior of composite magnetic alloys.