  Stability plays a central role in arithmetic. In this article, we explain
some basic ideas and present certain constructions for such studies. There are
two aspects: namely, general Class Field Theories for Riemann surfaces using
semi-stable parabolic bundles & for p-adic number fields using what we call
semi-stable filtered (phi,N;omega)-modules; and non-abelian zeta functions for
function fields over finite fields using semi-stable bundles & for number
fields using semi-stable lattices.
