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Is there any well written introduction for the modular space of complex structures on T^2?

Thank you!

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If you mean moduli space, then aren't the complex structures on the 2-torus known and parametrized? (Disclaimer: I am not a geometer, so might be missing something here.) – Yemon Choi Aug 30 '11 at 23:57
Yes, I know it known, but I need a good reference to understand. I think is upper half plane/ SL(2,Z) action. – user16750 Aug 31 '11 at 0:04
@jc: I think your comment is more appropriate as an answer. There is no obligation to make an answer to a reference request long or deep. – S. Carnahan Aug 31 '11 at 2:14
up vote 2 down vote accepted

As requested, I'm promoting this comment to an answer:

McKean and Moll's book "Elliptic curves" is a basic introduction to 2-tori with complex structure from the function theoretic, geometric, and arithmetic perspectives. What's closest to what you want is discussed in section 2.6 (on moduli of elliptic curves) and chapter 4 (on the modular group).

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Serre's "A course in arithmetic" is quite nice for this and everything else it covers.

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