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by tgb 3664 days ago
I started with Hubbard & Hubbard. It is truly wonderful (and based on Spivak's other calculus book), but I couldn't imagine learning it without either significant background or a formal class. Even with a 2 semester class devoted to it in college, I ended up not understanding the most advanced concepts (eg. differential forms) until years later when it finally came up again in graduate-level courses. Of course, it was really an excuse to learn to think mathematically, not to learn calculus on manifolds.