Axioms and Ordinals, An Introduction
This section presents ZF set theory,
as described by Zermelo
This is "standard" set theory, giving rise to the ordinals, integers, rationals,
reals, rings, fields, algebraic geometry, etc.
Other versions of set theory exist,
but I don't know anything about them.
Several axioms combine with logic
and the membership relation to build set theory.
Thus set theory is the study of propositional calculus with one relation.
Here come the axioms.