This is the second semester course of Complex Analysis. We will start with a complete proof of the Riemann mapping theorem. Then we switch to Harmonic Function Theory, Schwarz Reflection Principle, Elliptic Functions. After these, we study the Riemann-Zeta function and prove the Prime Number Theorem. We will also give a modern treatment of the Monodromy Theorem. After all these classical topics, we present a detailed discussion to Riemann Surfaces Theory, including the proof of the classical Riemann-Roch theorem. If time permitting, we also present the original proof of Poincare-Kobe Theorem.
our own notes, distributted during the lectures
501, 503. Basic topology