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Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.

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Chapter 1. Topological Spaces.- Chapter 2. Continuity and Products.- Chapter 3. Connectedness.- Chapter 4. Convergence.- Chapter 5. Countability axioms.- Chapter 6. Compactness.- Chapter 7. Topological Constructions.- Chapter 8. Separation Axioms.- Chapter 9. Paracompactness and Metrisability.- Chapter 10. Completeness.- Chapter 11. Function Spaces.- Chapter 12. Topological Groups.- Chapter 13. Transformation Groups.- Chapter 14. The fundamental Group.- Chapter 15. Covering Spaces.

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TEJ BAHADUR SINGH is an Emeritus Professor at the Department of Mathematics, University of Delhi, India, which he joined in 1989. Earlier, he served at the University of Allahabad and Atarra P.G. College, Banda, India. He received his Ph.D. from the University of Allahabad in 1983. With more than 40 years of teaching experience, he has written several research articles on the cohomological theory of compact transformation groups and has successfully guided eight M.Phil. and Ph.D. students. His primary research interest is in algebraic topology. He has taught various courses, including point-set topology, field theory, module theory, representation of finite groups, algebra, calculus, geometry, linear algebra, and real analysis.

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