Moduli spaces and their Picard group. The determinant bundle. The case of vector bundles: the linear system $|\mathcal{L}|$ and its geometry, the $\theta$ divisor of a vector bundle.

References

A. Beauville. Vector Bundles on Curves and Generalized Theta Functions: Recent Results and Open Problems. Current topics in complex algebraic geometry, MSRI Publications 28, 17-33; Cambridge University Press (1995).