I intend to cover aspects of the classical theory of complex multiplication, mainly from a modular point of view. A basic knowledge of algebraic number theory and the theory of modular forms will be helpful.
Topics I hope to treat include the generation of abelian extensions of imaginary quadratic fields by singular moduli, which are j-values at cm points, application to the class number 1 problem, traces of singular moduli as Fourier coefficients of weakly holomorphic modular forms of weight 3/2 and the Gross-Zagier formula for norms of singular moduli.