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Algebraic Topology is a branch of Mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. This book is useful for the post graduate students of Mathematics and it contains the concepts of Fundamental Group, Covering Space, Retraction, Fixed Point, The Borsuk - Ulam Theorem, Deformation Retract, Homotopy Type and The Seifert - Van Kampen Theorem.