An updated edition, Equivalents of the Axiom of Choice, II, was published as volume 116 of the same series in 1985.
This book codified the project of classifying theorems of mathematics according to whether the axiom of choice was necessary in their proofs, or whether they could be proven without it.
[4] It also includes more recent developments on the independence of the axiom of choice, and an improved account of the history of Zorn's lemma.
[2] Reviewer Chen Chung Chang writes that it "will be useful both to the specialist in the field and to the general working mathematician", and that its presentation of results is "clear and lucid".
[3] By the time of the second edition, reviewers J. M. Plotkin and David Pincus both called this "the standard reference" in this area.