Best book for theoretical multivariable calculus self-study

[PhysicsPrincess]

Hi,

I'm looking for a good book to study multivariable calculus from that would fit a proof-based undergraduate math course.
The emphasis should be on RIGOROUS proofs, theorems and presentation of concepts.
I really need a book that would be approachable for self-study with clear and easy-to-follow explanations and examples.

Can you recommend the best book? Thank you! :)

 

[KiggenPig]

I have heard that Michael Spivak's Calculus on Manifolds is a pretty good book, not as good as his single variable calculus book but still pretty good and rigorous.

 

[Xiuh]

I like Spivak, but I don't think it is suitable for self-study (it is VERY concise). I always recommend:
-Fleming - Functions of Several Variables
https://www.amazon.com/dp/0387902066/?tag=pfamazon01-20
-Munkres - Analysis on Manifolds
https://www.amazon.com/dp/0201315963/?tag=pfamazon01-20
-Edwards - Advanced Calculus of Several Variables
https://www.amazon.com/dp/0486683362/?tag=pfamazon01-20

 

[Anama Skout]

No one mentioned Hubbard?