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Allen Hatcher seems impossible and this is set as the course text?

So was wondering is there a better book than this? It's pretty cheap book compared to other books on amazon and is free online.

Any good intro to Algebraic topology books?

I can find a big lists of Algebraic geometry books on here. On a very old thread on Maths overflow someone recommended that a person should read James Munkres Topology first, then you should read Allen Hatcher book.

It just seems like Rudin's book but crammed with ten times more material.

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    Why don't you please indicate what your background is? The alg. topology book by Hatcher is generally so well-regarded that your description of it seeming impossible suggests a mismatch between its intended audience and what you bring to the table as a reader, rather than the book itself really being impossible.2011-11-22
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    For general topology everything up to Tychonoff theorem in Munkres Topology. I suppose I don't like the first chapter of the book. It seems weird to start with it and the pictures use seem misleading. It's free online and so that could explain why it is well-regarded.2011-11-22
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    The free-online-ness is definitely a plus, but/and Hatcher is a very good mathematician (so can be trusted about mathematical _fact_), and is a better writer than most! There is little reason to object to the choices made in the text, also. One may disagree, as with anything, but Hatcher has put his efforts (and non-collection of royalties, for example) "where his mouth is". And, specifically, I find nothing at all wrong with his choices, presentation, style, etc. It may be more fluid than some styles of 50 years ago, but that's a _good_ thing.2011-11-22
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    Hatcher's book is very well-written with a good combination of motivation, intuitive explanations, and rigorous details. It would be worth a decent price, so it is very generous of Dr. Hatcher to provide the book for free download. But if you want an alternative, Greenberg and Harper's Algebraic Topology covers the theory in a straightforward and comprehensive manner. It also contains significantly less discussion of motivation and intuition that you seem to dislike, though it does have a nice discussion of the functorial approach to algebraic topology.2011-11-22
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    I think most people will have to "edit" Hatcher as they read through it. There are many examples and motivational remarks that are hard to digest during a first pass, but for which one is very grateful later on. At any rate, two unmentioned alternatives are [Bredon](http://books.google.com/books/about/Topology_and_Geometry.html?id=G74V6UzL_PUC) and [Fulton](http://books.google.com/books?id=4khJg2wSxeMC). I hope you find something that suits you.2011-11-22
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    @simplicity: Like almost every book I have seen on algebraic topology, Hatcher's text is a *graduate text*. Your other questions posted on this site show that you are still learning undergraduate level algebra and topology. Until you have learned these subjects very well, I suspect you will find any algebraic topology text extremely to prohibitively challenging.2011-11-22
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    I also found Hatcher's book hard to digest at first, so I began reading Massey's "Basic Course..." alongside it. Massey's text is pretty much the opposite; very algebraic and formal (which I like). The main problem is probably the large amount of typos, but still a very good book IMO. I would also say that as you become more "aware" of what's going on in alg. topology, you might start to appreciate Hatcher's book even more.2011-11-22
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    @Ryan: Your comment above has been flagged as "rude" twice now, I think. While I agree with what you're saying, perhaps the phrasing could have been better - would you be okay with removing it?2011-11-29
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    My comment was considered a little rude, and I admit it was a little rude but I also think the participants deserve it considering how carelessly written the question is, and considering some of the comments and answers. Let me try to say the same thing in a different way. Hatcher's text is aimed at a more mature audience than the Munkres text. Perhaps the fact that it's free gives some people incentive to use it as a textbook when they should be aiming at less fully-developed introduction to the subject. But making claims about it being impossible or lacking in rigor is ridiculous.2011-11-29
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    Ironically, making such claims is pretty rude!2011-11-30
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    @simplicity: you have asked a few hours ago how to compute the dimension of a matrix algebra: that makes it clear that you are not in the intended audience of Hatcher's book (this is not a judgement on you but simply the statement of a fact) The thing is, your question is written in a tone rather incompatible with this fact; if Hatcher's book is the textbook for a course, that probably means you should wait a bit before taking it, not that the book is «impossible».2011-11-30
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    No one has pointed to it yet: www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf by J P May2013-03-17
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    Its good some people are interested in answering the question rather than being offended, "Its not a judgement .. but fact". Really? Why do people need to defend Hatcher like he's some sort of deity, I'm sure Hatcher himself wouldn't even mind pointing people to other books.2014-01-25
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    Kind of amazing how much acrimony was aroused by a student expressing a personal preference for a certain style of exposition. I understand why Hatcher's book is popular, but I'm baffled that people can't see why it would also put off some *students* who are used to very linear developments and very detailed arguments. This is a situation where the opinions of students are more important than those of experts; experts have subtle pedagogical blind spots due to their unconscious proficiency with a subject and the fact that they are often exceptionally smart.2015-03-08
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    Its easy to forget the precise way in which we came to learn things which are now second nature. Finally, there is an issue of impartiality, since many of these experts (whom I respect enormously) personally know the author of the text in question. This last fact is the only thing I think could account for the stridency of some of the responses.2015-03-08
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    My issue with Hatcher is that he sometimes relies on a strong geometric intuition that I do not share, while sometimes presenting the algebra in, IMO, an over-complicated way. I much prefer the text of May, which is Concise, but still clearer to me.2017-11-29

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