In 1963, the first author introduced a course in set theory at the University
of Illinois whose main objectives were to cover G6del's work on the con­


sistency of the Axiom of Choice (AC) and the Generalized Continuum


Hypothesis (GCH), and Cohen's work on the independence of the AC and


the GCH. Notes taken in 1963 by the second author were taught by him in


1966, revised extensively, and are presented here as an introduction to


axiomatic set theory.