Im beginner in algebraic topology.I have read the general topology book by Munkres and topology without tears by Morris

I have seen the Allen Hatcher book .It is very tough book ,so i need some easier book

I need references for very basic books in Algebraic topology and that book must contain given topics below

$1.$Homotopy Theory. Covering spaces, homotopy maps, homotopy equivalence,Contractible spaces, deformation retraction.

$2.$Fundamental Groups: Universal cover and lifting problem for covering maps, Fundamental groups of S1 and Sn.

$3$ .Introduction to Homology Theory.

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    $\begingroup$ Try "A First Course in Algebraic Topology" by Czes Kosniowski. Lots of figures but writes proofs better than Hatcher, overall very friendly. $\endgroup$
    – Ivo Terek
    Dec 26, 2020 at 21:14
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    $\begingroup$ Assuming you know point-set topology (basic definitions of topologies, open/closed sets, continuity, product/quotient/subset/disjoint union topologies) I would still recommend Hatcher. You might start with parts of the appendices for background material. $\endgroup$
    – pancini
    Dec 26, 2020 at 21:18
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    $\begingroup$ @IvoTerek good book ,i will try this book for $ 1/3$ week...after that i will give my feeback about this book on this comment $\endgroup$
    – jasmine
    Dec 26, 2020 at 21:40
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    $\begingroup$ try "topology of surfaces" for a very introduction before diving into a more classic book $\endgroup$ Dec 26, 2020 at 22:46
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    $\begingroup$ @IvoTerek I really enjoy this book wonderful books more better explaination than Allen hatcher book... $\endgroup$
    – jasmine
    Mar 6, 2021 at 20:07

1 Answer 1


Spanier, Greenburg and Harper, and Munkres are three that come to mind.

There was also one by Fomenko and somebody else (maybe Fuchs) on homotopy theory that had great illustrations.

  • $\begingroup$ The poster asked for an easier book than Hatcher, and I don't think Spanier qualifies. ;) $\endgroup$ Dec 27, 2020 at 1:20
  • $\begingroup$ You're probably right. But it is the subject itself that is inherently difficult. I am partial to Spanier. He's one of the best professors I ever had. I had a copy of it, but no longer (after all I've been through). @JohnPalmieri $\endgroup$
    – user403337
    Dec 27, 2020 at 1:28

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