4 February 0) Introduction 1) The modular group 2) Modular forms on SL(2,Z) 3) Lattices in C 4) Eisenstein series 11 February 5) Gamma\H as a Riemann surface 6) The structure of the ring of modular forms 7) The j-function 18 February 8) The product formula for Delta 9) Modular forms and elliptic curves 25 February 10) Hecke operators for SL(2,Z) 11) The Petersson product 12) Eigenforms for the Hecke algebra 4 March 13) Euler products 14) More on the Hecke algebra 11 March 15) L-functions 18 March 16) Subgroups of finite index 17) Modular forms on congruence subgroups 25 March 18) Dimensions of spaces of modular forms 1 April 19) Eisenstein series 20) Hecke operators on congruence subgroups 8 April 21) Hecke operators 22) Changing levels 22 April 23) Atkin-Lehner theory