TITLE: Mazur's torsion theorem on elliptic curves and its generalisations
QUESTION [7 upvotes]: I want to study Mazur's torsion theorem for elliptic curves over $Q$ and its generalizations for number fields, i.e., papers by Kamienny, Kenku & Momose, Filip Najman. So please suggest to me what background I should have before starting to read the relevant papers. If you could offer me some books/papers/articles, I would be glad.

REPLY [14 votes]: Andrew Snowden has just finished teaching a course on Mazur's torsion theorem--video-taped lectures and extensive notes may be found here.  I've watched several of the lectures; they are excellent.

REPLY [4 votes]: The general case over arbitrary number fields has been treated by Loïc Merel.  A good place to start would be Bas Edixhoven's Bourbaki exposé Rational torsion points on elliptic curves over number fields, Séminaire Bourbaki, 36 (1993-1994), Exposé No. 782.
There is also an excellent set of notes by Joseph Œsterlé which were to be found on the ICTP website.