1 What is Topology? Euler's Theorem 2 New Surfaces Orientability Dimension Two More Surfaces The Klein Bottle3 The Shortest Moebius Strip4 The Conical Moebius Strip5 The Klein Bottle6 The Projective Plane Symmetry7 Map Coloring8 Networks The Koenigsberg Bridges Betti Numbers Knots9 The Trial of the Punctured Torus10 Continuity and Discreteness "The "Next Number" Continuity Neighborhoods Limit Points11 Sets Valid or Merely True? Venn Diagrams Open and Closed Sets Transformations Mapping Homotopy In Conclusion Appendix Index