Analytic functions and the Cauchy-Riemann equations, calculus of residues including evaluation of real integrals, power and Laurent series, conformal mappings and the Riemann mapping theorem, the Dirichlet and Neumann problems, functions of bounded order and product expansions, the Riemann zeta function, elliptic functions. This is a more rigorous version of MAT 342 intended for math majors, in particular math majors in advanced track program.