Front Cover -- First Concepts of Topology: The Geometry of Mappings of Segments, Curves, Circles, and Disks -- Copyright Page -- Contents -- Introduction -- Part I: Existence Theorems in Dimension 1 -- 1. The first existence theorem -- 2. Sets and functions -- 3. Neighborhoods and continuity -- 4. Open sets and closed sets -- 5. The completeness of the real number system -- 6. Compactness -- 7. Connectedness -- 8. Topological properties and topological equivalences -- 9. A fixed point theorem -- 10. Mappings of a circle into a line -- 11. The pancake problems -- 12. Zeros of polynomials -- Part II: Existence Theorems in Dimension 2 -- 13. Mappings of a plane into itself -- 14. The disk -- 15. Initial attempts to formulate the main theorem -- 16. Curves and closed curves -- 17. Intuitive definition of winding number -- 18. Statement of the main theorem -- 19. When is an argument not a proof? -- 20. The angle swept out by a curve -- 21. Partitioning a curve into short curves -- 22. The winding number W(φ, γ) -- 23. Properties of A(φ, γ) and W(φ, γ) -- 24. Homotopies of curves -- 25. Constancy of the winding number -- 26. Proof of the main theorem -- 27. The circle winds once about each interior point -- 28. The fixed point property -- 29. Vector fields -- 30. The equivalence of vector fields and mappings -- 31. The index of a vector field around a closed curve -- 32. The mappings of a sphere into a plane -- 33. Dividing a ham sandwich -- 34. Vector fields tangent to a sphere -- 35. Complex numbers -- 36. Every polynomial has a zero -- 37. Epilogue: A brief glance at higher dimensional cases -- Solutions for Exercises -- Index -- Back Cover.