This graduate text introduces relativistic quantum theory, emphasising its important applications in condensed matter physics. Basic theory, including special relativity, angular momentum and particles of spin zero are first reprised. The text then goes on to discuss the Dirac equation, symmetries and operators, and free particles. Physical consequences of solutions including hole theory and Klein’s paradox are considered. Several model problems are solved. Important applications of quantum theory to condensed matter physics then follow. Relevant theory for the one electron atom is explored. The theory is then developed to describe the quantum mechanics of many electron systems, including Hartree-Fock and density functional methods. Scattering theory, band structures, magneto-optical effects and superconductivity are among other significant topics discussed. Many exercises and an extensive reference list are included. This clear account of relativistic quantum theory will be valuable to graduate students and researchers working in condensed matter physics and quantum physics.