I first learned about manifolds through Introduction to Smooth Manifolds by John M. Lee. The book is dense but beautifully structured, guiding you from basic topology to smooth maps and tangent spaces with clear logic. It demands focus, yet every definition builds toward a deeper picture of how geometry works beneath the surface. Highly recommended.

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WhyOhWhyQ 2 days ago | parent | next [-]

It's truly the best book on Smooth Manifolds, though if you'd like a gentler approach which is still useful, then I suggest Loring Tu's books. Lee's Topological Manifolds book is also very nice. His newest edition of the Riemannian manifolds book requires selective reading or it'll slow you down.

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perihelions 2 days ago | parent | next [-]

What's the relation between the different Lee manifolds? Is it a sequence you're supposed to read in order?

	▲	ducttapecrown 2 days ago \| parent [-]
		Lee taught Intro to Topological Manifolds for one quarter, and then the next two quarters where Intro to Smooth Manifolds. Then Riemannian, then vector bundles, and then complex manifolds.

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tamnd 2 days ago | parent | prev [-]

That's a great suggestion. I actually started with Topological Manifolds before moving on to Introduction to Smooth Manifolds and it really helped build a solid foundation.

I havent read Loring Tus books before but let me look at them since I have been wanting to revisit the topic with a clearer and more relaxed approach.

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codethief 2 days ago | parent | prev [-]

Tbh, I never quite understood the appeal of John M. Lee's book. It's not bad but I didn't find it great, either, especially (IIRC) in terms of rigor. Meanwhile, the much less well-known "Manifolds and Differential Geometry" by Jeffrey M. Lee (yeah, almost the same name) was much better.