TITLE: fonctions-faisceaux correspondence 
QUESTION [11 upvotes]: what are the standard references for this subject, i.e., the realization of functions as traces of Frobenius acting on sheaves?  Is there any motivation or philosophy coming from categorification, number theoretic analogies, or other directions?

REPLY [2 votes]: My preferred reference is Kiehl and Weissauer's book (very complete, and in English).
Of course, if you want motivation, you can read my blog post (this the companion to the one Thomas linked to).