In the first chapter of the book, we give an introduction to the theory of one-parameter operator semigroups. We begin with the splitting theorem of Jacobs- Deleeuw-Glicksberg and the Eberlein mean ergodic theorem for a one-parameter operator semigroup. Then we present the elementary theory of
-semigroups and discuss some relations between spectral properties of the generator of a
- semigroup and its asymptotic behavior. We follow the standard textbooks , , , , , , , and send the reader for other deep and delicious topics of this theory to those books and to , , , , . In the last section, we discuss the asymptotically finite-dimensional semigroups. We use frequently well-known results from operator theory and functional analysis, and send the reader to standard textbooks , , , and  for them.