  Peter Aczel’s book (1988) treats many axioms that contradict FA, but it pays most attention to AFA.  It also proved many of the important results in the subject, including ones mentioned in this entry.  Aczel’s own entrance to the subject was an area of semantic modeling that he had been working on, concerning the calculus of communicating systems (CCS).  He found it natural to propose a set theoretic semantics, and yet the most obvious modeling seemed to run into problems with Foundation.  It is always a bold step to recommend changing the axioms of set theory in order to make an application of the subject.  Usually it is a brash move.  For the most part people resist the idea: when the proposal might well be cast in more standard forms (as can be done with work using AFA), people wonder why one wants to tamper with a standard theory; when it cannot be cast in a standard way, the reception is even worse.