Content: The course's core topics are the following:

• The modular group and the upper half-plane
• Modular forms of level 1 and the valence formula
• Eisenstein series, Ramanujan's Delta function
• Congruence subgroups and fundamental domains, modular forms of higher level
• Hecke operators
• The Petersson scalar product, old and new forms
• Statement of multiplicity one theorems
• The L-function of a modular form
• Modular symbols

Books:

F. Diamond and J. Shurman, A First Course in Modular Forms, Graduate Texts in Mathematics 228, Springer-Verlag, 2005. (Covers everything in the course and a great deal more, with an emphasis on introducing the concepts that occur in Wiles' work)

J.-P. Serre, A Course in Arithmetic, Graduate Texts in Mathematics 7, Springer-Verlag, 1973. (Chapter VII is a short but beautifully written account of the first part of the course which is good introductory reading)

W. Stein, Modular Forms, A Computational Approach, Graduate Studies in Mathematics, American Mathematical Society, 2007. (Emphasis on computations using the open source software package Sage)