This is a list of axioms as that term is understood in mathematics, by Wikipedia page. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system.
These are the de facto standard axioms for contemporary mathematics
See also Zermelo set theory.
With the Zermelo-Frankel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable
Equivalents of AC
Weaker than AC
Alternates incompatible with AC
Other axioms
