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I want to read the theory of fibre bundle, vector bundle and principal G bundle. Also about classifying spaces. Can someone suggest me good references for this material.

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    $\begingroup$ Maybe you can check out Dale Husmoller's "Fibre bundles" $\endgroup$ Commented Jan 17, 2018 at 15:22
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    $\begingroup$ R. Cohen has a good set of notes "The Topology of Fiber Bundles", which are free online if you google for them. $\endgroup$
    – Tyrone
    Commented Jan 17, 2018 at 15:42

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I would suggest to have a look at :

  • Topology of Fiber bundles by Steenrod
  • Topology and groupoids by Ronald Brown ( this text is also free for download in pdf format if you google search)
  • Foundations of Differential Geometry by Nomizu and Kobayashi ( not a very good text to learn from but it is considered the encyclopedia of differential geometry).
  • A User's Guide to Algebraic Topology by Dodson.
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