Contents -- Preface -- 1 The equational theory of -terms for finite R-trivial semigroups Jorge Almeida and Marc Zeitoun -- 1. Introduction -- 2. R-trees and R-automata -- 3. Periodicity and the word problem for -terms -- 4. Equations for -terms -- 5. Canonical forms -- 6. Comparison with related work of Bloom and Choffrut -- Acknowledgments -- References -- 2 Some results on Cerny type problems for transformation semigroups D.S. Ananichev and M.V. Volkov -- 1. Motivation and overview -- 2. Semigroups of orientation preserving or orientation reversing transformations -- 3. Semigroups of order preserving or order reversing transformations -- References -- 3 Near permutation semigroups Jorge M. Andre -- 1. Introduction -- 2. Preliminaries -- 3. Regular near permutation semigroups -- 4. Near permutation semigroups generated by two groups -- Acknowledgements -- References -- 4 The origins of independence algebras Joao Araujo and John Fountain -- 1. A Heuristic Approach to Independence Algebras -- 2. Thoughts of Independence in Poland -- 3. The Description of Independence Algebras -- 4. Independence Algebras and Semigroups -- Acknowledgements -- References -- 5 Abelian kernels, solvable monoids and the abelian kernel length of a finite monoid Manuel Delgado and Vitor H. Fernandes -- 1. Introduction and Preliminaries -- 1.1. Kernels and related properties -- 1.2. On some transformation monoids -- 2. The abelian kernel length of a solvable monoid -- 3. On some inverse monoids -- 4. On some non-inverse monoids -- Acknowledgments -- References -- 6 Braids and factorizable inverse monoids David Easdown, James East and D.G. Fitz-Gerald -- 1. Introduction -- 2. The Merge and Part Braid Monoid -- 3. Coset Monoids of Groups and Duality -- 4. An Embedding in the Coset Monoid of the Braid Group -- References.

7 Hyperbolic groups and completely simple semigroups John Fountain and Mark Kambites -- 1. Hyperbolic Groups -- 2. Multiplication Tables of Finitely Generated Groups -- 3. Word Hyperbolic Semigroups -- 4. Completely Simple Semigroups -- Acknowledgements -- References -- 8 An introduction to E*-unitary inverse semigroups - from an old fashioned perspective Donald B. McAlister -- 1. Introduction and pre-history -- 2. History: E-unitary inverse semigroups. -- 3. The Present: E*-unitary inverse semigroups -- Acknowledgments -- References -- 9 Turan's graph theorem and maximum independent sets in Brandt semigroups J.D. Mitchell -- 1. Introduction -- 2. The main result -- 3. Final remarks -- Acknowledgments -- References -- 10 On semilattices of archimedean semigroups - a survey Melanija Mitrovic -- 0 . Introduction -- 1. Preliminaries -- 2. Semilattices of Nil-extensions of Simple Semigroups -- 3. Semilattices of Left Strongly Archimedean Semigroups -- 4. Semilattices of Left Completely Archimedean Semigroups -- 5. Semilattices of Nil-exstensions of Simple and Regular Semigroups -- 6. Semilattices of Completely Archimedean Semigroups -- References -- 11 Relative rewriting systems S.J. Pride and Jing Wang -- 1. Rewriting Systems and Ideal Pairs -- 2. Finite Derivation and Homological Types (FDT and FHT) -- 3. Relative Rewriting Systems over Groups -- 4. Proof of Theorem 4 -- References -- 12 Inverse semigroups acting on graphs James Renshaw -- 1. Introduction -- 2. The Group Case -- 3. Partial Actions of Inverse Semigroups -- 3.1. Introduction -- 3.2. Stabilisers and -cosets -- 3.3. L-classes and free partial acts -- 3.4. Generators and relations -- 4. Graphs -- 4.1. S-graphs -- 4.2. Graphs of Inverse Semigroups -- 5. Summary -- Acknowledgement -- References -- 13 A modern approach to some results of Stiffler Benjamin Steinberg.

1. Introduction and Main Results -- 2. The Proofs of Theorems 1.2 and 1.3 -- 2.1. Maximal proper quotients -- 2.2. R-faithful morphisms -- 2.3. Proof of Theorem 1.2 -- 2.4. Proof of Theorem 1.3 -- References.