These are lecture notes from an introduction to axiomatic set theory taught by Scott Weinstein in the spring of 2009, typed up by me and Vilhelm Sjoberg. I make no guarantees whatsoever as to their completeness or correctness! A PDF for each individual lecture is provided below; you can also download all the lecture notes in one big PDF.

1/21 Well orderings
1/26 Ordinals, transfinite induction
1/28 Transfinite recursion, cardinals
2/2 Cardinals (Axiom of Choice, cardinality, normal functions, cofinality, cardinal arithmetic)
2/4 More cardinals (regularity, the Continuum Hypothesis, Koenig's theorem)
2/9 The real line (partial isomorphisms, Cantor's back-and-forth theorem, uniqueness of the reals, the Cantor set)
2/11 The real line, part II (perfect sets, Cantor-Bendixson theorem)
2/16 Introduction to relative consistency results (Axiom of Regularity, transitive closure, relativization, absoluteness)
2/18 A digression on absoluteness (elementary substructures, Mostowski's Collapsing Lemma, nonstandard (non-well-founded) models, completeness and compactness of first-order logic, Lowenheim-Skolem Theorem, Skolem's paradox)
2/23 Proof of the Lowenheim-Skolem Theorem and related results
2/25 More relative consistency: consistency of ZF - Reg implies consistency of ZF.
3/2 Strongly inaccessible cardinals and ZF.
3/16 Midterm exam review.
3/18 The reflection principle.
3/23 The constructible hierarchy, formal definition (encoding formulas as sets, satisfiability, Delta-1)
3/25 The constructible hierarchy, part II (More Delta-1, absoluteness of L, almost universal, L models ZF)
3/30 The constructible hierarchy, part III (inner models, ZF + (V=L) proves AC)
4/1 The constructible hierarchy, part IV (ZF + (V=L) proves GCH)
4/6 Independence of CH from ZFC (partial orders, filters, P-genericity)
4/8 Independence of CH (cardinal preservation, antichains, ccc, quasi-disjointness)
4/13 Independence of CH (more ccc and preservation of cardinals, P-names)
4/15 Independence of CH (generic extensions, properties of generic extensions, forcing, Truth, Definability)
4/20 Independence of CH (M[G] is a ctm, digression on Kripke-Platek set theory, axiom of Collection, and computability)
4/22 Independence of CH (finish proof that M[G] is a ctm), Ramsey's theorem
4/27 Ramsey cardinals