A First Course in Modular Forms, by Diamond and Shurman (D-S), is many people's favourite; not sure if it is too advanced. Also, Serre's course in arithmetic has something (chapter VII) on Modular Forms. And Shimura's Elementary Dirichlet Series and Modular Forms is of more managable size than (D-S), but assumes more familiarity with algebraic number theory than Serre.
