Informal Topology -- Graphs -- Surfaces -- Graphs and Surfaces -- Knots and Links -- The Differential Geometry of Surfaces -- Riemann Geometries -- Hyperbolic Geometry -- The Fundamental Group -- 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.