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| Mathematics Before Euclid | |
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| The Empirical Nature of pre-Hellenic Mathematics | |
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| Induction Versus Deduction | |
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| Early Greek Mathematics and the Introduction of Deductive Procedures | |
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| Material Axiomatics | |
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| The Origin of the Axiomatic Method Problems | |
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| Euclid's Elements | |
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| The Importance and Formal Nature of Euclid's Elements | |
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| Aristotle and Proclus on the Axiomatic Method | |
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| Euclid's Definitions, Axioms, and Postulates | |
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| Some Logical Shortcomings of Euclid's Elements | |
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| The End of the Greek Period and the Transition to Modern Times Problems | |
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| Non-Euclidean Geometry | |
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| Euclid's Fifth Postulate | |
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| Saccheri and the Reductio ad Absurdum Method | |
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| The Work of Lambert and Legendre | |
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| The Discovery of Non-Euclidean Geometry | |
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| The Consistency and the Significance of Non-Euclidean Geometry Problems | |
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| Hilbert's Grundlagen | |
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| The Work of Pasch, Peano, and Pieri | |
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| Hilbert's Grundlagen der Geometrie | |
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| Poincar�'s Model and the Consistency of Lobachevskian Geometry | |
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| Analytic Geometry | |
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| Projective Geometry and the Principle of Duality Problems | |
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| Algebraic Structure | |
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| Emergence of Algebraic Structure | |
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| The Liberation of Algebra | |
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| Groups | |
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| The Significance of Groups in Algebra and Geometry | |
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| Relations Problems | |
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| Formal Axiomatics | |
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| Statement of the Modern Axiomatic Method | |
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| A Simple Example of a Branch of Pure Mathematics | |
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| Properties of Postulate Sets--Equivalence and Consistency | |
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| Properties of Postulate Sets--Independence, Completeness, and Categoricalness | |
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| Miscellaneous Comments Problems | |
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| The Real Number System | |
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| Significance of the Real Number System for the Foundations of Analysis | |
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| The Postulational Approach to the Real Number System | |
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| The Natural Numbers and the Principle of Mathematical Induction | |
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| The Integers and the Rational Numbers | |
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| The Real Numbers and the Complex Numbers Problems | |
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| Sets | |
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| Sets and Their Basic Relations and Operations | |
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| Boolean Algebra | |
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| Sets and the Foundations of Mathematics | |
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| Infinite Sets and Transfinite Numbers | |
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| Sets and the Fundamental Concepts of Mathematics Problems | |
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| Logic and Philosophy | |
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| Symbolic Logic | |
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| The Calculus of Propositions | |
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| Other Logics | |
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| Crises in the Foundations of Mathematics | |
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| Philosophies of Mathematics Problems | |
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| The First Twenty-Eight Propositions of Euclid | |
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| Euclidean Constructions | |
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| Removal of Some Redundancies | |
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| Membership Tables | |
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| A Constructive Proof of the Existence of Transcendental Numbers | |
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| The Eudoxian Resolution of the First Crisis in the Foundations of Mathematics | |
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| Nonstandard Analysis | |
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| The Axiom of Choice | |
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| A Note on G�del's Incompleteness Theorem Bibliography | |
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| Solution Suggestions for Selected Problems | |
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| Index | |