In light of increasing uses for direct numerical approximations of Maxwell's equations in science and engineering, this text provides mathematics graduate students and researchers with a theoretical foundation for finite element methods in computational electromagnetism. Monk (mathematical sciences, U. of Delaware) emphasizes finite element methods for scattering problems involving the solutions of Maxwell's equations on infinite domains. The book's main focus is on an error analysis of edge finite element methods that are well suited to Maxwell's equations. The book concludes with a short introduction to inverse problems in electromagnetism.