There are many different generalizations of modular forms. One has Hilbert modular forms, Siegel modular forms, Maass wave forms, Jacobi forms, and then there are various generalities of automorphic forms. There are level structures and weights, there are adelic forms and cusp forms, and all sorts of algebraic groups and subgroups.
I'm having much trouble grasping all these different notions. Could someone perhaps give an overview of the various versions of modular and automorphic forms, along with their respective relevance? Specifically, I am interested in the Langlands conjecture, and its connection with homotopy theory (in which I have a reasonable background).