The book itself is good, as others have said, but I want to use this review let others know about different editions of the book. It appears that Pearson have derived the Pearson New International Edition from the American edition of the book by a) Removing all but the headings from the contents pages (reducing the length of the contents from 4 pages to 1). b) Removing the majority of the index pages (reducing the length of the index from 19 pages to 3). For example the letter H in the index contains only the following three entries: hemisphere; horizontal line; horizontal lines. (Note the conspicuous absence of, for instance, homotopy equivalence, homeomorphism and homomorphism, and note also that these terms do not appear in the single contents page either.) Conversely, the word Point IS included in the index as a single entry with about 150 different page numbers, followed by the word Points with another 150 page numbers. c) Placing Chapter 12 after Chapter 13. d) Removing the preface and note to the reader. As a result of these changes, the page numbering in the Pearson New International Edition differs by 2 from the American edition, except for Chapters 13 and 12 which are in the wrong order. Pearson have addressed this difference in page numbers by adding a second page number to each page, so that, for example, page 487 (of the American edition) is numbered 487 at the top of the page and 453 at the bottom. The reduced contents and index pages refer to the second page number, the one at the bottom of the page. In contrast, the Eastern Economy Edition appears to be numbered exactly as the American edition, has detailed contents and index pages, and has an extra chapter, (Chapter 14 Applications to Group Theory) which is absent from the Pearson New International Edition. The Eastern Economy Edition is significantly cheaper than the Pearson New International Edition and this must partly be due to the lower quality paper and binding. However there are no issues with print quality as far as I can see, and the book is perfectly readable. The cover of the Eastern Economy Edition that I received was purple rather than green, but the design is the same as the American edition.
I used to own the red covered 1975's first edition of this title since the late 1990's, but quite recently purchased the new edition as well, and donated the old book to our campus library. Before anything else, let me express that from the many topology texts that I have come across over the years, this one easily stands out as the best rigorous introduction for a beginning graduate student. It covers all the standard material for a first course in general topology starting with a full chapter on set theory, and now in the second edition includes a rather extensive treatment of the elemantary algebraic topology. The style of writing is student-friendly, the topics are nicely motivated, (counter-)examples are given where they were needed, many diagrams provided, the chapter exercises relevant with the correct degree of difficulty, and there are virtually no typos. The 2nd edition fine-tunes the exposition throughout, including a better paragraph formatting of the material and also greatly expands on the treatment of algebraic topology, making up for 14 total chapters (as opposed to eight in the first edition). A notable minor issue in the first edition was the consistent usage of the third person masculine pronoun in the discussions, specially in the foreword, for addressing all possible readers of the book, but this has fortunately been revised in the 2000's edition. Eventhough a few contending general topology texts --such as a recent title published in the Walter Rudin Series-- have started to hit the academic markets, Munkres will no doubt remain as the classic, tried-&-trusted source of learning and reference for generations of mathematics students. The one thing that should be mentioned though, one would wish there were some more hints and answers provided, at the back of the book (at least to the harder problems), so as to make the text more helpful for those readers who use it for self-study. Also a reviewer has correctly mentioned here that Dr. Munkres does not include differential topology in his presentation. I speculate this is perhaps because he has already written a separate monograph on the topic. In fact, it is also necessary to get a handle on some fair amount of algebraic topology first, for a full-fledged coverage of the differential treatment. Regardless, one great reference for a rigorous and worthwhile excursion into the area (covering brief introductions to the Morse and cobordism theories as well), is the excellent title by Morris W. Hirsch, which is available on the Springer-Verlag GTM series. I would also like to mention that one other very decent book on general topology, which has unfortunately been out of print for quite some time, is a treatise by "James Dugundji" (Prentice Hall, 1965). The latter would nicely complement Munkres, as for example, Dugundji discusses ultrafilters and some more of the analytical directions of the subject. It's a real pity that The Dover Publications in particular, has not yet published this gem in the form of one of their paperbacks. The undergrad students testing the waters for the first time, should try Fred H. Croom's text, originally published in 1989 but now again re-issued. This title is closely modeled in exposition and selection of topics on Munkres, thus nicely serving as a prerequisite.
I have many books about topology, but found this the best introduction to the subject. The author succeeds in getting the reader hooked from begin to end without loosing mathematical rigor. Although this is a introduction the book goes much farther then most other books, so you get also a view of some deep theorems. Highly recommended.