The field of quantum plasmas has a long and diverse tradition and is becoming of increasing current interest, motivated by applications to micro-electronics and to focused high-power lasers. In this book, plasma kinetic theory is developed in a covariant (4-tensor) notation, which facilitates generalizations to include all relativistic and electromagnetic effects. Relativistic quantum effects are included by using quantum electrodynamics (QED) to calculate the plasma response 4-tenors. The effects of the plasma are included in QED by replacing the photon propagator in vacuo by that in the medium, such that the poles of this propagator correspond to the natural wave modes of the medium.