Algebra at the beginning of the twentieth century
Communication between east and west
Anton Kazimirovich Sushkevich
Unique factorisation in semigroups
Embedding semigroups in groups
The Rees theorem
The French school of 'demi-groupes'
The expansion of the theory in the 1940s and 1950s
The post-Sushkevich Soviet school
The development of inverse semigroups
Matrix representations of semigroups
Books, seminars, conferences, and journals
Appendix: Basic theory

The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed 'Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in the East and West, and the study of the extent to which contact between the two sides was possible.