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I am looking for an introductory book that explains the relations of topology and bundles.

I know a basic topology and algebraic topology. But I don't know much about bundles. I want a book that

  1. explains the definition of bundles carefully and give some intuition on bundles
  2. explains relations between topology and bundles
  3. has physics motivation (if possible)

If you know a good books, please let me know. Thank you very much in advance.

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    A book that's similarly encyclopedic bundles + basic algebraic topology to Kirk and Davis is Tammo tom Dieck's "Algebraic Topology".2012-10-19

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Steenrod's "The Topology Of Fibre Bundles" is a classic. It isn't particularly modern but it does the basics very well.

Husemoller's "Fibre Bundles" is a bit more modern and has a bit more of a physics-y outlook but still very much a book for mathematicians. I find it not as pleasant to read as Steenrod's book but it's fine.

Peter May has some nice notes on bundles and fibrations, available on his webpage. They're quite modern but not written with a physics outlook, very much the outlook of a topologist.