This book serves as a concise introduction to the theory of magnetism. It is written from the perspective of theoretical physics, which emphasizes general principles applicable across different branches of physics over technical details and narrow specialization. The fundamentals of magnetism are introduced starting at the level of a single magnetic dipole and its underlying mechanical object, the classical spin. From there, the book transitions to many interacting spins and a continuum description (field theory) that focuses on the universal aspects over long time scales and distances. The physical systems of interest are ferromagnets, simple antiferromagnets with 2 magnetic sublattices, and complex antiferromagnets with 3 or more sublattices.

The topics include their classical ground states, weakly excited states in the form of spin waves, and nonlinear excitations such as topological solitons. The mathematical description combines classical equations of motion with the principle of least action. Classical spin waves and solitons are quantized via the canonical procedure.

Each chapter includes problems. Solutions are provided at the end of the book. The book is aimed at graduate students entering the field of magnetism but can also be useful to postdocs and more senior researchers as a reference. The reader is assumed to be familiar with Lagrangian mechanics and canonical quantization.

Oleg Tchernyshyov, born in the Soviet Union, is a physicist renowned for his work on magnetic solitons. He earned a master’s degree in physics from Moscow Institute of Physics and Technology in 1990, followed by a Ph.D. from Columbia University in 1998. After postdoctoral fellowships, he joined Johns Hopkins University in 2002 as an assistant professor, rising to full professor in 2015. In 2019, he was elected a Fellow of the American Physical Society for his contributions to magnetic solitons' dynamics and collective coordinate formalism.