What are the best introductory texts on modular forms that are suited for a brief six week course intended for advanced undergraduates? The students will be quite sharp and as far as prerequisites go, they can be expected to have completed two courses in algebra and analysis each as well as a first course in complex analysis and a course in number theory at the level of Hardy & Wright.
I am considering Apostol's Modular Forms and Dirichlet Series in Number Theory but worry that it may not be possible to make serious progress in six weeks.
Best Answer
Perhaps it is a little too brisk for your purposes, but I have always liked Zagier's exposition in The 1-2-3 of Modular Forms (Springer Universitext) very much. It is about 100 pages, more than half of which are applications of various kinds and for various backgrounds; I'm sure it contains something for everyone.