TITLE: Where was Riemann Existence first proven?
QUESTION [5 upvotes]: 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)?

REPLY [9 votes]: 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".