Topology, as a subject, has become ubiquitous in almost every branch of Mathematics. It is now a core course at the Masters or Honours level in almost every university. This book develops the fundamental ideas and concepts of Topology, with an emphasis on topics and results that are needed in modern Topology and its applications to other disciplines. Salient Features : About the Authors : Vikram Aithal is a faculty at the Institute of Chemical Technology, Mumbai. He did his Ph.D. at IIT Bombay after which he held post-doctoral, teaching and visiting positions at various leading institutes in India and abroad. He has been associated with the MTTS Programmes for several years. S. Kumaresan is the first recipient of the Indo-Canadian Mathematics forum for Excellence in Teaching and Research. He is also the first recipient of the INSA Teaching Award for Mathematics. He did his Ph.D. at TIFR, Mumbai and then served as a Professor at the University of Mumbai and the University of Hyderabad. He has been a visiting Professor at many leading institutes both in India and abroad. He is known for founding the MathematicsTraining and Talent Search Programme. After retirement, he continues to teach mathematics and spread the knowledge through his very popular youtube channel. The focus is on core concepts of the subject, and can be used as a starting point for learning niche topics. A variety of examples are given. And used repeatedly to explain every new concept introduced. There are about 390 exercises scattered throughout the book. Hints and solutions are provided for all exercises. The exercises are of two types. Some within the chapter, to help motivate and understand the concepts introduced. Some at the end of the chapter, to help review and consolidate. Strategy and motivation for all proofs are given to enable diligent readers to work out details on their own. All concepts are developed keeping both students and teachers in mind.