The Quillen-Suslin Theorem was conjectured by J.-P Serre (see F.A.C) and proved (independently) by D. Quillen and A. A. Suslin.

There are several treatments on this theorem, namely Algebra by Serge Lang, A course in ring theory by D. Passman, and Serre’s problem on projective modules by T. Y. Lam.

Here I quote an account by A, Mathew.