The modular group and its subgroups, the fundamental domain. Modular forms,
examples, Eisenstein series, cusp forms. Valence (dimension) formula, Petersson
inner product. Hecke operators. L-functios: definition, analytic continution
and functional equation.
Suggested books and references:
Serre, J.P., A Course in Arithmetic, Graduate Texts in Mathematics no. 7
Koblitz, N., Introdution to Modular Forms
,Graduate Texts in Mathematics no. 97, Springer-Verlag, 1984.
Iwaniec, H., Topics in Classical Automorphic Forms
,Graduate Texts in Mathematics 17, AMS, 1997.
Diamond, F. and Schurman, J., A First Course in Modular Forms
,Graduate Texts in Mathematics no. 228, Springer-Verlag, 2005.