This paper continues the study of the Axiom of Choice by E. Zermelo [Neuer Beweis für die Möglichkeit einer Wohlordung, Math. Annalen, 65 (1908), 107-128; translated in van Heijenoort 1967, 183-198]. We prove some new equivalents of the Axiom of Choice, i.e., Zorn’s lemma, and in connection with an initial equivalent also fact that every set has at least three choice functions.