This course will cover a review of holomorphic and harmonic functions; topology of the space of holomorphic functions: series and infinite products, Weierstrass p-function, Weierstrass and Mittag-Leffler theorems; normal families: normal families and equicontinuity, theorems of Montel and Picard; conformal mappings: Riemann mapping theorem, Schwarz-Christoffel formula; Riemann surfaces: Riemann surface associated with an elliptic curve, inversion of an elliptic integral, Abel's theorem. Further topics may be included such as analytic continuation and monodromy theorem.