Arithmetic on modular curves

Question

I had tried to read the first few pages of Glenn Stevens' Arithmetic on Modular Curves, but it is somehow extremely unreadable to me, the text format is odd and stating too much facts without explanation.

I think I might lack some background, so is there any other books which explain more on some similar topics or could help me understanding Glenn Stevens' Arithmetic on Modular Curves ?

Here is its table of contents:

Ps. I had read Serre's A course in Arithmetic, and have some basic knowledge of algebraic number theory.

Answer 1

Stevens' 1982 book is a research monograph, aimed at readers who are already experts. There's a big gap between it and Serre's book.

To bridge that gap, you might like to try reading some of the articles in the Cornell--Silverman--Stevens volume on Fermat's last theorem (especially Rohrlich's article in that volume on modular curves). That and the references therein should help you to understand what's going on in Arithmetic on Modular Curves.

Answer 2

Another good reference is Diamond and Shurman's "A First Course in Modular Forms", or William Stein's "Modular Forms".