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This is a postgraduate level textbook, written specifically for use at universities in India and fills a long-felt need. It has several welcome features. Motivation and heuristic explanations are provided before introducing many of the concepts; bases and subbases of a topology are given more attention than most books do; both filters and nets are treated in great details and there is also a discussion on the so-called equivalence of the two concepts; gives a detailed treatment of image and quotient topologies. Compactification is treated in far greater detail than any other book, with ample warnings about common pitfalls. The presentation of compactifications is rigorous and yet easier to understand. The chapter on Uniform Spaces proceeds at a pace that the student will find easier to handle. A large number and a broad spectrum of exercises are given at the end of each chapter. The introductory chapter has a list of over a hundred set-theoretic identities which the student should find very handy as a reference list. There is an extensive bibliography for the library-oriented student. An excellent index of keywords and another of notations make the job of searching and cross-referencing easy. The first edition and the subsequent revised edition of this book have been remarkably well received.

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