"The Dirac Equation" is a modern presentation of the realistic quantum mechanics of electrons intended to make new mathematical results accessible to a wider audience. It treats in some depth the relativistic invariance of a quantum theory, self-adjointness and spectral theory, qualitative features of relativistic bound and scattering states, and the external field problem in quantum electrodynamics, without neglecting the interpretational difficulties and limitations of the theory. A novel feature is the extensive use of supersymmetric quantum mechanics in the discussions of, e.g. the nonrelativistic limit, Fredholm and Witten indices, the relativistic Coulomb problem, particles with anomalous moments, behaviour in the presence of magnetic fields, and soliton theory. The book is aimed at scientists and graduate students interested in quantum mechanics who want to learn about the mathematical foundations, the physical interpretation and important applications of Dirac's electron theory.