This will be a year-long introductory course in the classical theory of holomorphic functions of one variable. The text will be Conway's book Functions of One Complex Variable, Volume 1.

Topics: Complex numbers. Infinite Series. The exponential function. Holomorphic functions. Cauchy theory. Elementary consequences of the Cauchy integral formula. The residue calculus. Meromorphic functions. The Gamma function. Normal families. Conformal mapping. Runge's theorem. Theorems of Mittag-Leffler and Weierstrass. Analytic continuation. Riemann surfaces. Picard's theorem. Further topics as time permits.