I am familiar (to an extent) with the theory of compact Riemann surfaces without boundary, but I am interested in the theory of compact Riemann surfaces with boundary.

To what extent do the following ideas/results generalize?

* Riemann-Roch theorem
* Abel's theorem
* The Riemann-Hurwitz formula
* The classification of holomorphic line bundles

The literature seems to be a little sparse on this particular subject, so any suggestions would be appreciated.