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I believe Visual Group Theory - Nathan Carter is the best book for a non-mathematician (with high school math) to learn Group Theory.

Could someone please recommend me a similar book (if there is) to learn Topology?

Edit: I know many books in Topology, but someone who has read the above book will know what kind of reference I'm asking for. I am not looking for hard exercises, but to learn the concept and use it.

Thanks.

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    $\begingroup$ Nice question and nice book. $\endgroup$ – user63181 Nov 19 '13 at 21:49
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For general topology I would very much advise the book Topology by James R. Munkres.

I wouldn't be able to advise you very well for a book of algebraic topology, because I'm just learning the subject myself. Probably a good place where to start are Algebraic Topology by Hatcher (available online) and Topology and Geometry by Bredon.

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  • $\begingroup$ maybe an even better place to start is spanier's algebraic topology ;). also in many aspects better than munkres is kelley $\endgroup$ – Alexander Grothendieck Nov 19 '13 at 23:33
  • $\begingroup$ @000 I don't know the books of Spanier and Kelley, but I've already heard the names. What I really enjoyed about Munkres is the way he exposes the theory: you always know what he's doing/trying to do. $\endgroup$ – Daniel Robert-Nicoud Nov 19 '13 at 23:37
  • $\begingroup$ spanier is THE book on algebraic topology, and the only reason for reading hatcher and bredon instead is not being able to spanier (which is much more algebraic) $\endgroup$ – Alexander Grothendieck Nov 19 '13 at 23:50
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    $\begingroup$ My god, please do not start learning algebraic topology with Spanier. It is a great reference for those who algebra know the subject, but it is awful to learn from. $\endgroup$ – Potato Nov 20 '13 at 2:02
  • $\begingroup$ haters gonna hate $\endgroup$ – Alexander Grothendieck Nov 20 '13 at 16:34
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Intuitive Topology by Prasolov

The book has tons of illustrations (it's hard to find a page without one, most have two!). According to the abstract it should be accessible to advanced high school students. And it's not expensive: less than $16.

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Try A Topological Picturebook by George K. Francis.

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Czes Kosniowski's A First Course in Algebraic Topology changed my life.

Hatcher and Munkres are also wonderful, but in any case, it's likely that the answers you will receive will correspond to the answerers' respective introductions to the subject.

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H. Graham Flegg's From Geometry to Topology is a gentle and liberally-illustrated introduction to topology, starting from congruence classes in geometry. The final chapters of the book overlap, intentionally (see author's preface), with the beginning of most books/courses on general topology. However, I should point out that the book is not a substitute for a more standard textbook. It's more of a bridge to such books.

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For differential topology:

  1. Bott and Tu "Differential forms in algebraic topology",

  2. Guillemin and Pollack "Differential Topology",

  3. Milnor "Morse theory".

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  • $\begingroup$ These are great books, but I wouldn't say they are similar to Carter's Visual Group Theory. $\endgroup$ – J W Apr 27 '14 at 10:24
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Topology -James Munkres I have been using James Munkres book for self study. The proofs are well presented ,easy to follow and yet still rigorous. The first few chapters give you Set Theory concepts to prepare you for the rest of the book

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