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I am looking for a textbook(s) that discusses differential geometry, smooth manifolds etc. More precisely, I have been trying to find a textbook that covers the following topics:

  1. Differential geometry ( vector fields, forms, manifolds, mappings between manifolds, bundles, etc)
  2. Fibre bundle application to physics
  3. Lie theory and differential geometry
  4. Includes (or has some) illustrations

I am looking for something that is rigorous but not completely terse like a pure mathematics book, but also not so physical. I have found Marian's Fecko's book good however, the whole idea of working out and deriving definitions is not something I am particularly fond of. I have also read Isham's text and found myself needing to look up a lot of things to fill in the gaps.

Qmechanic
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    Nakahara's Topology, Geometry, and Physics has everything that you describe and more and is terrific! – Rokas Veitas Mar 13 '24 at 21:24
  • Possible duplicates: https://physics.stackexchange.com/q/29956/2451 ad links therein. – Qmechanic Mar 13 '24 at 22:22
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    I will give a piece of advice. Usually physicists want to learn math, but they look for something which is “more like Physics style”. I recommend avoiding this mindset and really studying the math as it is. This will allow you later on to use it in a much better way. That said my suggestion is Spivak’s “A Comprehensive Introduction to Differential Geometry”. Isham’s book can also come in handy. – Gold Mar 13 '24 at 22:45
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    My usual advice for this question is not a book, but the lectures of Frederic Schuller: General Relativity and Geometric Anatomy of Physics. They are not books, but they are quite complete and give you the base understanding and confidence to read technical books on the subject. They are mathematical in nature, but make connections to physics (e.g., the GR lectures are 12 lectures of math, followed by 12 lectures of their applications in GR). – Ben H Mar 14 '24 at 00:32

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