Relativistic Many Body Theory : A New Field Theoretical Approach From the Contents: Introduction Time Independent Formalism Time Dependent Formalism S Matrix Greens Functions Covariant Evolution Operator and Greens Operator Numerical Illustrations to Part II Covariant Evolution Combined With Electron Correlation. 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. This is a procedure on an intermediate level frequently u sed in recent time by chemists on molecular systems where a full QED treatment is out of question. Part II describes three methods for QED calculations a) the standard S matrix formulation b) the Two times Green’s function method developed by the St Petersburg Atomic Theory group and c) the Covariant evolution operator (CEO) method recently developed by the Gothenburg Atomic Theory group. In Part III the CEO method is combined with electron correlation to arbitrary order to a unified MBPT QED procedure. The new Part IV includes two new chapters dealing with dynamical properties and how QED effects can be evaluated for such processes. This part is much needed as there has been an increasing interest in the study of QED effects for such processes. 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.