I would like to ask if there exist pedagogical expositions of the Mordell-Weil theorem ([wikipedia](http://en.wikipedia.org/wiki/Mordell%E2%80%93Weil_theorem)). What parts of number theory (algebraic geometry) one should better learn first before starting to read a proof of Mordell-Weil? 



Proofs of Mordell-Weil theorem
J. Silverman and J. Tate "The rational points on elliptic curves" is a wonderful introduction to elliptic curves over rational numbers. It covers topics such as Mordell-Weil, Nagell-Lutz Theorem, elliptic curves over finite fields, etc.


For more advanced treatment of Mordell-Weil, I suggest the following textbook:


J. Silverman "The arithmetic of elliptic curves" (Chapter 8 is about Mordell-Weil).


