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Preface. Acknowledgment. 1. Informal Topology. 2. Graphs. 3. Surfaces. 4. Graphs and Surfaces. 5. Knots and Links. 6. The Differential Geometry of Surfaces. 7. Riemann Geometries. 8. Hyperbolic Geometry. 9. The Fundamental. 10. General Topology. Appendix A: Curves. Appendix B: A Brief Survey of Groups. Appendix C: Permutations. Appendix D: Modular Arithmetic. Appendix E: Solutions and Hints to Selected Exercises. References and Resources. Index.