Modular forms have been thrust into mathematical prominence by Wiles’ proof of Fermat’s Last Theorem. Wiles in actuality proved a special case of the Shimura-Taniyama conjecture, which relates elliptic curves and modular forms.

Fred Calegari has written a nice introduction to the topic of modular forms in the guise of a book review of A first course in modular forms by Diamond and Shurman. (The review also features the best variant of the “kids today” sentiment I’ve seen recently: “With today’s Ipod generation more likely to study elliptic curves and modular forms before learning any class field theory…”