In its half-century history, the theory of semigroups has grown from modest attempts to generalize both group theory and ring theory in the direction of a single binary operation obeying only the associative law to the present stage of an independent branch of algebra with a large body of important results.
The first books on semigroup theory represented attempts to systematize most of the knowledge on the subject, whereas later works have tended to cover only some particular areas. One of the areas of semigroup theory which showed great popularity almost from its beginning is that of inverse semigroups. The present book represents the first attempt to systematize the principal parts of the theory of inverse semigroups. Not all results in this area are included, but the main subjects are treated in complete detail from elementary definitions to the frontier of the existing state of the art.