The theory of one-parameter semigroups of linear operators on Banach spaces started in the ?rst half of this century, acquired its core in 1948 with the Hille–Yosida generation theorem, and attained its ?rst apex with the 1957 edition of Semigroups and Functional Analysis by E. Hille and R.S. Phillips. In the 1970s and 80s, thanks to the e?orts of many di?erent schools,thetheoryreachedacertainstateofperfection,whichiswellrep- sented in the monographs by E.B. Davies [Dav80], J.A. Goldstein [Gol85], A. Pazy [Paz83], and others. Today, the situation is characterized by manifold applications of this theory not only to the traditional areas such as partial di?erential eq- tions or stochastic processes. Semigroups have become important tools for integro-di?erentialequationsandfunctionaldi?erentialequations,inqu- tum mechanics or in in?nite-dimensional control theory. Semigroup me- ods are also applied with great success to concrete equations arising, e.g., in population dynamics or transport theory. It is quite natural, however, that semigroup theory is in competition with alternative approaches in all of these ?elds, and that as a whole, the relevant functional-analytic toolbox now presents a highly diversi?ed picture. At this point we decided to write a new book, re?ecting this situation but based on our personal mathematical taste. Thus, it is a book on se- groups or, more precisely, on one-parameter semigroups of bounded linear operators. In our view, this re?ects the basic philosophy, ?rst and strongly emphasized by A. Hadamard (see p. 152), that an autonomous determin- tic system is described by a one-parameter semigroup of transformations.