Table of Contents

• I. GENERAL TOPOLOGY.
• 1. Set Theory and Logic.
• 2. Topological Spaces and Continuous Functions.
• 3. Connectedness and Compactness.
• 4. Countability and Separation Axioms.
• 5. The Tychonoff Theorem.
• 6. Metrization Theorems and Paracompactness.
• 7. Complete Metric Spaces and Function Spaces.
• 8. Baire Spaces and Dimension Theory.
• II. ALGEBRAIC TOPOLOGY.
• 9. The Fundamental Group.
• 10. Separation Theorems in the Plane.
• 11. The Seifert-van Kampen Theorem.
• 12. Classification of Surfaces.
• 13. Classification of Covering Spaces.
• 14. Applications to Group Theory.
• Index.