  This is an integrated part of our Geo-Arithmetic Program.
  In this paper we initiate a geometrically oriented construction of
non-abelian zeta functions for curves defined over finite fields by a weighted
count of semi-stable bundles. Basic properties such as rationality and
functional equation are established. Examples of rank two zetas over genus two
curves are given as well. Based on this and motivated by our study for
non-abelian zetas of number fields, general non-abelian $L$ functions for
function fields are defined and studied using Langlands and Morris' theory of
Eisenstein series.
