TITLE: Source: Coherent locally free sheaves and projective modules
QUESTION [5 upvotes]: What is a good and very quick and concise article for the proof of the equivalence of the categories of locally free sheaves on $\mathrm{Spec}(A)$ and finitely generated projective $A$-modules?

REPLY [4 votes]: Why not read Serre's crystal-clear article which introduced this equivalence?
As Gauss said: "Read the masters".