  We introduce new non-abelian zeta functions for curves defined over finite
fields. There are two types, i.e., pure non-abelian zetas defined using
semi-stable bundles, and group zetas defined for pairs consisting of (reductive
group, maximal parabolic subgroup). Basic properties such as rationality and
functional equation are obtained. Moreover, conjectures on their zeros and
uniformity are given. We end this paper with an explanation on why these zetas
are non-abelian in nature, using our up-coming works on 'parabolic reduction,
stability and the mass'.
  The constructions and results were announced in our paper on 'Counting
Bundles' arXiv:1202.0869.
