A reference book discussing applications of formal language theory to group theory, particularly geometric and computational group theory.

Derek F. Holt is a professor of mathematics at the University of Warwick. He authored the successful Handbook of Computational Group Theory, which has now become the standard text in the subject, and he co-authored The Maximal Subgroups of Low-Dimensional Groups (with John N. Bray and Colva M. Roney-Dougal, Cambridge, 2013). Holt was also one of five co-authors of the seminal book Word Processing in Groups (1992) on the theory of automatic groups, and has contributed mathematical software to the Magma and GAP systems. In 1981, he was awarded the London Mathematical Society Junior Whitehead Prize.

Preface; Part I. Introduction: 1. Group theory; 2. Formal languages and automata theory; 3. Introduction to the word problem; Part II. Finite State Automata and Groups: 4. Rewriting systems; 5. Automatic groups; 6. Hyperbolic groups; 7. Geodesics; 8. Subgroups and co-set systems; 9. Automata Groups; Part III. The Word Problem: 10. Solubility of the word problem; 11. Context-free and one-counter word problems; 12. Context-sensitive word problems; 13. Word problems in other language classes; 14. The co-word problem and the conjugacy problem; References; Index of notation; Index of names; Index of topics and terminology.