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This book is devoted to the theory of electrodynamic phenomena in systems under an external magnetic field. The analysis is based on Maxwell's equations. We present the fundamentals of magnetostatics, quasistatic electromagnetic fields and electromagnetic wave propagation. The main part of the book describes the behaviour of a charged particle in an electromagnetic field, and the electrodynamics of plasmas, liquid crystals and superconductors. These very different subjects have an important common feature, namely the fundamental role played by the magnetic field. Plasmas, liquid crystals and superconductors can be considered as magnetoactive media, because their electromagnetic characteristics are strongly affected by an external magnetic field. The book will be useful for graduate students in physics, experimentalists, and engineers in high-tech industries.