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I am self-studying algebraic topology and I was wondering which book is better for my purposes. The second part of Munkres' topology deals with algebraic topology and it seems easier to understand, but I see that Hatcher is almost always the go-to textbook for the subject. However I have been having a lot of trouble with Hatcher's exercises. Can anyone with knowledge on the subject tell me which book is better suited for self study, in terms of better understanding the theory and having the better exercises?

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  • $\begingroup$ If you have trouble, I would say that is the authors fault, not the readers fault, the real question is if there is a better book available, and unfortunately I cannot help with that. But I would say, don't torture yourself, look for something that you like better, if Hatcher doesn't work. I don't know algebraic topology, ended up teaching it once with only one student (so I had to teach both myself and the student), tried to use Hatcher (was a new book then) and didn't particularly like it. Someone wrote they don't like Munkres' style,neither do I, but I have nothing to recommend instead... $\endgroup$
    – Mirko
    Mar 27, 2021 at 1:53
  • $\begingroup$ I do not own Munkres but i've spent a considerable amount of time with Hatcher's book. I think it's an incredibly great book, however, many concepts, even if pictured and organized very well are rather hard to fully understand if you are actually purely self-studying without any exposure to some concepts in a proper lecture. That's just my personal experience though. After i attended a lecture where certain concepts where explained in greater detail, i really appreciated Hatcher's book. $\endgroup$
    – Zest
    Mar 28, 2021 at 5:30

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This is not really an answer to your question. Since you asked a soft question, call this a soft answer.

Many students, especially those who do not have some background in turning pictures into proofs (which should be taught in any first topology class but is usually not) struggle with Hatcher, as he expects a lot of these very rapid steps. A recent question also suggests that difficulty with manipulating quotient spaces.

I do not have an opinion about whether the text of the book itself is the right one for you. (Personally, I think it may be worthwhile to struggle a bit with it, but if you're not learning from it it's not ideal to waste your time. Personally, I dislike Munkres' writing. This is my taste and nothing more.)

However, Hatcher's exercises are among the most insightful introductory algebraic topology exercises I know. I think that you should do them. I think that if you're having difficulty, that strongly suggests that you could learn a lot from them! I would suggest doing the exercises no matter what books (or combination thereof; I see no harm in using multiple references, as they may explain concepts in different language, some of which may be more helpful for you) you ultimately study from.

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Munkres book is good for self study but in Refferences Book we can't understand all concept so you do self study if you not understand then share here

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