Eddy Current Approximation of Maxwell Equations : Theory algorithms and applications This book deals with the mathematical analysis and the numerical approximation of time harmonic eddy current problems. It is self contained and suitable for mathematicians and engineers working in the field and also accessible for beginners. Depending on the choice of the physical unknowns these problems are formulated in different variational ways with specific attention to the topology of the computational domain. Finite elements of nodal or edge type are used for numerical approximation and a complete analysis of convergence is performed. A specific feature of the book is the emphasis given to saddle point formulations in terms of the magnetic and electric fields. New results for voltage or current intensity excitation problems are also presented. Setting the problem A mathematical justification of the eddy current model Existence and uniqueness of the solution Hybrid formulations for the electric and magnetic fields Formulations via scalar potentials Formulations via vector potentials Coupled FEM BEM approaches Voltage and current intensity excitation Selected applications.