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


As requested, I'm promoting this comment to an answer: McKean and Moll's book "Elliptic curves" is a basic introduction to 2tori 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). 


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

