Ever since its invention in 1929 the Dirac equation has played a
fundamental role in various areas of modern physics and mathematics. Its
applications are so widespread that a description of all aspects cannot
be done with sufficient depth within a single volume. In this book the
emphasis is on the role of the Dirac equation in the relativistic
quantum mechanics of spin-1/2 particles. We cover the range from the
description of a single free particle to the external field problem in
quantum electrodynamics. Relativistic quantum mechanics is the
historical origin of the Dirac equation and has become a fixed part of
the education of theoretical physicists. There are some famous textbooks
covering this area. Since the appearance of these standard texts many
books (both physical and mathematical) on the non- relativistic
Schrodinger equation have been published, but only very few on the Dirac
equation. I wrote this book because I felt that a modern, comprehensive
presentation of Dirac's electron theory satisfying some basic
requirements of mathematical rigor was still missing.