This book introduces recently developed ideas and techniques in semigroup theory to provide a handy reference guide previously unavailable in a single volume. The opening chapter provides sufficient background to enable the reader to follow any of the subsequent chapters, and would by itself be suitable for a first course in semigroup theory. The second chapter gives an account of free inverse semigroups leading to proofs of the McAlister P-theorems. Subsequent chapters have the underlying theme of diagrams and mappings, and the new material includes the theory of biordered sets of...