This revised second edition of the author's classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title.  In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes.

The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions.

The main text is divided into three parts. In Part I, the standard time-independent and time-dependent perturbation procedures are reviewed. This includes a new section at the end of chapter 2 concerning the so-called "Fock-space procedure" or "Coulomb-only procedure" for relativistic-QED calculations

All methods treated in the book are illustrated with numerical examples, making it a text suitable for advanced students new to the field and a useful reference for established researchers.

"The book provides a first-time unified perspective based upon quantum field theory and illustrated with several numerical examples. Many chapters were re-edited, with improved writing from the author's original text." (Eric Howard, Contemporary Physics, October, 29, 2018)