Review of "Algebraic and automata-theoretic properties of formal languages" by Seymour Ginsburg. North Holland, 1975.

Theoretical computer science presents to mathematicians a rather peculiar sight. There are various chunks that have a good deal of internal organization, e.g. finite automata, context free languages, Krohn-Rhodes theory and a few others. Then there are also isolated oases (sometimes teeming with activity) but without much contact with each other. In this situation any new idea that will help bring a few of these isolated chapters under a common roof is highly welcome. One such idea dawned on Seymour Ginsburg and Sheila Greibach in August 1966. The idea took the form of the definition of an AFL ( : Abstract Family of Languages). Until then people talked about individual families without a general definition of what properties a good' family should have. It soon became apparent that all of the sufficiently evolved families of languages hitherto considered satisfy the axioms for an AFL or one of its few modifications.