Actually, this is the main page for the different forms of the axiom of choice. Each such form is really a class of equivalencies, represented by a summary statement (which includes a statement and a corresponding Howard-Rubin number), and a list of results that are equivalent to the given form. Each of these results has its own statement, along with comments, and references to articles, books, and the separate notes available on this website.

"The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes."
— Bertrand Russell