Differential geometry, what book is good for a first timer?

AI Thread Summary
The discussion centers on the topic of manifold theory and the prerequisites for studying it. Participants express curiosity about the terminology associated with manifolds and seek guidance on suitable introductory texts. A recommendation is made for "Calculus on Manifolds" by Spivak, which is deemed appropriate for those with a background in metric spaces and basic topology. For readers with the necessary foundational knowledge, "Differential Topology" by Guillemin and Pollack is suggested as a rigorous option that effectively proves theorems, aligning with the desire for a solid mathematical foundation.
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I've been wanting to see what this topic is all about for awhile now. I see the word "Manifold" and other terminology floating around on the forum. It got me really curious.

I wonder what the prerequisites are to reading a book like this?

Hypothetically I have the prerequisites, what would you recommend for a first time read?

I care about how rigorous the book is in proving theorems. Something unfounded wouldn't be worth reading.
 
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