  The aim of this paper is to present an algebro-geometric approach to the
study of the geometry of the moduli space of stable bundles on a smooth
projective curve defined over an algebraically closed field $k$, of arbitrary
characteristic. This establishes a bridge between the arithmetic approach of
Harder, Narasimhan et al. and the gauge group approach of Atiyah and Bott. One
of the basic ideas is to consider a notion of divisor of higher rank and a
suitable Abel-Jacobi map generalizing the classical notions in rank one.
