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What's

Is there a good place to learn about the structure of moduli stack of G-bundles flat $G$-bundles on a (complex) an algebraic curve?

Of course, we're just studying representations of a group $\pi_1(X)\to G$ modulo some conjugation (that's why it should be a stack). Since this is very similar to Galois representations in number theory, I wonder if there's a reference that also explains the similarities and differences between the two cases.

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# Moduli space of flat bundles

What's a good place to learn about the structure of moduli stack of G-bundles on a (complex) algebraic curve?