The book provides a comprehensive treatment of the physics of hysteresis in magnetish, and of the mathematical tools used to describe it. The relations of hysteresis to Maxwell's equations, equilibrium and non equilibrium thermodynamics, non-linear system dynamics, micromagnetics and domain theory are discussed from a unified viewpoint. These aspects are then applied to the interpretation of magnetization reversal mechanisms: coherent rotation and switching in magnetic particles, stochastic domain wall motion and the Barkhausen effect, coercivity mechanisms and magnetic viscosity, rate-dependent hysteresis and eddy-current losses. Emphasis is given to the connection between basic physical ideas and phenomenological models of interest to applications, and, in particular, to the conceptual path going from Maxwell's equations abnd thermodynamics to micro-magnetics and to Preisach hysteresis modeling.