I've tried several times to read up on modular curves, and I've despaired every time. It seems that there are several competing narratives, that all get enfused and conspire to befuddle me. There are modular forms, automorphic forms, Hecke theory, L-functions, Galois representations, hyperbolic space, primitive forms, Fuchsian groups, the Langlands program and so forth.

It is somewhat of an introductory question, but I would be very grateful if one of you could put things in some sort of order, and separate the narratives. (What generalizes what, what is parrallel to what, and what implies what)

I've tried several times to read up on modular curves, and I've despaired every time. It seems that there are several competing narratives, that all get infused and conspire to befuddle me. There are modular forms, automorphic forms, Hecke theory, L-functions, Galois representations, hyperbolic space, primitive forms, Fuchsian groups, the Langlands program and so forth.

It is somewhat of an introductory question, but I would be very grateful if one of you could put things in some sort of order, and separate the narratives. (What generalizes what, what is parrallel to what, and what implies what?)