  This article is based on lecture notes prepared for the August 2006 Cologne
Summer School. The first part contains background material and references for
beginners. The second (and main) part is a survey of the current status in the
theory of pluri-theta linear series and generalized theta divisors on moduli
spaces of vector bundles on curves. It emphasizes relatively new techniques
employed in the analysis of linear series on these moduli spaces, namely the
use of moduli spaces of stable maps for understanding Quot schemes, and the
Fourier-Mukai functor in the study of coherent sheaves on abelian varieties. In
addition, it briefly describes recent important developments, most significant
of which is the proof of the Strange Duality conjecture due to Belkale and
Marian-Oprea.
