Nowadays the standard reference for Riemann's Existence theorem is SGA1, where the proof heavily relies on Serre's GAGA. I imagine that the theorem is much older, as its name suggests, and that its original proof is quite different. I thought it would be instructive for me to look at how this theorem was viewed in the pre-SGA era.


### Question


Where does a proof of Riemann's Existence Theorem original appear? Or better yet, where is a readable summary of it in English (or somewhat less preferably in French)?



Where was Riemann Existence first proven?
The original source for the modern version is


H.Grauert and R. Remmert, Komplexe Räume, Math.Ann. 136 (1958), 245–318.


I don't know of an exposition in English.


The version due to Riemann was just for algebraic curves. This is covered in many sources; my favorite is Narasimhan's book "Compact Riemann Surfaces".


