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An Introduction to Set Theory and Topology
These notes are an introduction to set theory and topology. Topics covered includes: Sets, Pseudometric Spaces, Topological Spaces, Completeness and Compactness, Connected Spaces, Products and Quotients, Separation Axioms, Ordered Sets, Ordinals and Transfinite Methods, Convergence and Compactifications.
Author(s): Ronald C. Freiwald, Washington University in St. Louis
459 Pages 
This note describes the following topics: Propositional calculus, Well orderings and ordinals, Posets and Zorns lemma, Predicate logic, Set theory, Cardinals and incompleteness.
Author(s): I B Leader
70 Pages
Descriptive Set Theory by David Marker
This note covers the following topics: Classical Descriptive Set Theory, Polish Spaces, Borel Sets, Effective Descriptive Set Theory: The Arithmetic Hierarchy, Analytic Sets, Coanalytic Sets, Determinacy, Hyperarithmetic Sets, Borel Equivalence Relations, Equivalence Relations, Tame Borel Equivalence Relations, Countable Borel Equivalence Relations, Hyperfinite Equivalence Relations.
Author(s): David Marker
105 Pages
Set Theory Some Basics And A Glimpse Of Some Advanced Techniques
Goal of these notes is to introduce both some of the basic tools in the foundations of mathematics and gesture toward some interesting philosophical problems that arise out of them. Topics covered includes: Axioms and representations, Backbones and problems, advanced set theory.
Author(s): Toby Meadows
91 Pages
This note covers the following topics: Logic, Elementary Set Theory, Generic Sets And Forcing, Infinite Combinatorics, Pcf, Continuum Cardinals.
Author(s): J. Donald Monk
602 Pages