Richard Borcherds: Modular forms

This is a 13-lecture course, with each lecture being about 30 minutes or so, given online by Richard Borcherds. It gives an introduction to modular forms.

1. Introduction
2. Eisenstein series
3. Fourier coefficients of Eisenstein series
4. Fundamental domain
5. Classification
6. Modular functions
7. Discriminant and E₂
8. Theta functions
9. Theta functions in higher dimensions
10. Hecke operators
11. Product formula for j
12. Hecke operators for forms
13. Petersson inner product