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1 What is Topology? Euler's Theorem 2 New Surfaces Orientability Dimension Two More Surfaces The Klein Bottle 3 The Shortest Moebius Strip 4 The Conical Moebius Strip 5 The Klein Bottle 6 The Projective Plane Symmetry 7 Map Coloring 8 Networks The Koenigsberg Bridges Betti Numbers Knots 9 The Trial of the Punctured Torus 10 Continuity and Discreteness "The "Next Number" Continuity Neighborhoods Limit Points 11 Sets Valid or Merely True? Venn Diagrams Open and Closed Sets Transformations Mapping Homotopy In Conclusion Appendix Index