If you want to learn calculus in a rigorous way, I'd recommend Spivak's Calculus book. After that, there are a lot of ways to branch off into theoretical mathematics (point-set topology, linear algebra, multivariable analysis, combinatorics, abstract algebra etc.) so it really depends on what you want to learn.

If I were you, I'd read through Spivak's Calculus, and then a good linear algebra book. I've heard Axler's book recommended, but if you've seen some basic linear algebra already then I'd recommend Hoffman and Kunze for a more rigorous treatment. After reading a linear algebra book, you're interests should be well defined enough for you to pick a next book to read.