A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Mike Paterson, and William Thurston.
[1][2][3] The book is divided into two parts, one on the basic theory of these structures and another on recent research, connections to geometry and topology, and other related topics.
[1][4] More generally, reviewer Gilbert Baumslag recommends it "very strongly to everyone who is interested in either group theory or topology, as well as to computer scientists."
Baumslag was an expert in a related but older area of study, groups defined by finite presentations, in which research was eventually stymied by the phenomenon that many basic problems are undecidable.
[3] In 2009, mathematician Mark V. Lawson wrote that despite its "odd title," the book made automata theory more respectable among mathematicians stating that it became part of "a quiet revolution in the diplomatic relations between mathematics and computer science".