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Set theory and the structure of arithmetic
The purposes of this book is, first, to answer the question 'What is a number?' and, of greater importance, to provide a foundation for the study of abstract algebra, elementary Euclidean geometry and analysis. This book covers the following topics: The elements of the theory of sets, The Natural Numbers, The Integers and the Rational Numbers and the Real Numbers.
Author(s): Norman T Hamilton
286 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
Set Theory by Victoria University of Wellington
This PDF covers the following topics related to Set Theory : Introduction, Well-orders and Ordinals, Classes and Transfinite Recursion, Cardinals, Zorn’s Lemma, Ramsey’s Theorem, Lo´s’s Theorem, Cumulative Hierarchy, Relativization, Measurable Cardinals, Godel’s Constructible Universe, Banach-Tarski Paradox.
Author(s): Victoria University of Wellington
60 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