Modular forms and string theory

1. Introduction

Part I. Modular Forms and their Variants:

2. Elliptic functions

3. Modular forms for SL(2,Z)

4. Variants of modular forms

5. Quantum fields on a torus

6. Congruence subgroups and modular curves

7. Modular forms for congruence subgroups

8. Modular derivatives and vector-valued modular forms

9. Modular graph functions and forms

Part II. Extensions and Applications:

10. Hecke operators

11. Singular moduli and complex multiplication

12. String amplitudes

13. Toroidal compactification

14. S-duality of type IIB superstrings

15. Dualities in N = 2 super Yang-Mills theories

16. Basic Galois theory.