This course is an introduction to axiomatic set theory and its methods. Set theory is a foundation for practically every other area of mathematics and is a deep, rich subject in its own right. The course will begin with the Zermelo-Fraenkel axioms and general set constructions. Then the natural numbers and their arithmetic are developed axiomatically. The central concepts of cardinality, cardinal numbers, and the Cantor-Bernstein theorem are studied, as are ordinal numbers and transfinite induction. The Axiom of Choice and its equivalents are presented along with applications.