Inverse semigroups: the theory of partial symmetries
Published by World Scientific in 1998.
I am now working on a Second Edition (2024).
I hope it will see the light of day next year.

This book sets out to develop the theory of inverse semigroups taking Ehresmann's theory of ordered groupoids as its jumping off point.
It includes accounts of the theory of tiling semigroups, introduced by Johannes Kellendonk, together with other applications.


 

Finite automata
Published by CRC Press in 2003.

This is a textbook intended for both mathematicians and computer scientists.
The first half of the book, which is more CS oriented, deals with Kleene's Theorem and minimisation;
the second half of the book, which is more maths oriented, deals with the Eilenberg-Schutzenberger correspondence
which links varieties of regular languages with  pseudovarieties of finite monoids. 
A solution book is available from the publishers.




Handbook of Networked and Embedded Control Systems
Edited by Dimitrios Hristu-Varsakelis and William S. Levine, published by Birkhauser in 2004.
I wrote the chapter entitled Finite Automata, pp 117-143.




Algebra & geometry: an introduction to university mathematics
Published by CRC Press in 2016.

This book is intended to be a bridge between school and university mathematics.
I therefore hope that it will be useful to pupils in school studying A-levels/Advanced Highers
and their equivalents as well as to first year mathematics students.
A solution book is available from the publishers.





Wagner's theory of generalised heaps
With C. D. Hollings, Springer, 2017.
I wrote Chapter 9, a mathematical essay on Wagner's main paper.





A first course in logic
Published in September 2018 published by CRC Press.





Algebra & Geometry: second edition
To be published on 23rd June 2021.
This edition varies from the first in the inclusion of some essays
and an additional eleventh chapter which describes how to construct the real numbers
from the rationals.