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This groundbreaking new text: presents Euclidean, abstract, and basic algebraic topology; explains metric topology, vector spaces and dynamics, point-set topology, surfaces, knot theory, graphs and map coloring, the fundamental group, and homology; includes worked example problems, solutions, and optional advanced sections for independent projectsFollowing a path that will work with any standard syllabus, the book is arranged to help students reach that "Aha!moment, encouraging readers to use their intuition through local-to-global analysis and emphasizing topological invariants to lay the groundwork for algebraic topology.