This monograph provides a systematic treatment of theabstract theory of adjoint semigroups. After presenting thebasic elementary results, the following topics are treatedin detail: The sigma (X, X )-topology, -reflexivity, the Favard class, Hille-Yosida operators, interpolation andextrapolation, weak -continuous semigroups, the codimensionof X in X , adjoint semigroups and the Radon-Nikodymproperty, tensor products of semigroups and duality, positive semigroups and multiplication semigroups. The major part of the material is reasonably self-containedand is accessible to anyone with basic knowledge of semi-group theory and Banach space theory. Most of the resultsare proved in detail. The book is addressed primarily toresearchers working in semigroup theory, but in view of the"Banach space theory" flavour of many of the results, itwill also be of interest to Banach space geometers andoperator theorists.