Pre-reqs for graph theoretic Hurwitz Groups

[aLearner]

So I'm trying to understand this paper (found here: http://arxiv.org/abs/1301.3411) but my math skills are very limited.
These include:

-Groups (the very basics, like the first of Charles Pinter's book)
-Analysis (the very basics)

But what all books/papers/topics would you suggest I become familiar with so as to genuinely understand the paper?

Your help is most appreciated.
-
aLearner

 

[verty]

I think if you know chapters 13-16 in Pinter very well, you will be able to make sense of a lot of that paper.