Monstrous Moonshine
A very tidy abstract:
"Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms, and vertex operator algebras. Moonshine beyond the Monster, the first book of its kind, describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between modern mathematics and mathematical physics."
conceals a very inquisitive approach, concluding
"So, has Monstrous Moonshine been explained? According to most of the fathers of the subject, it hasn't. . . .We are entering a consolidation phase, tidying up, generalising, simplifying, clarifying, working out more examples, climbing a few metres higher. Important and interesting discoveries will be made in the next few years, and yes, there still is mystery. . ."
Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics, by Terry Gannon. Cambridge, UK; New York: Cambridge University Press, 2006. Link to MnCat Record