I Complex Analysis in One Variable. - 1 Elementary Theory of Holomorphic Functions. - 2 Covering Spaces and the Monodromy Theorem. - 3 The Winding Number and the Residue Theorem. - 4 Picard's Theorem. - 5 Inhomogeneous Cauchy-Riemann Equation and Runge's Theorem. - 6 Applications of Runge's Theorem. - 7 Riemann Mapping Theorem and Simple Connectedness in the Plane. - 8 Functions of Several Complex Variables. - 9 Compact Riemann Surfaces. - 10 The Corona Theorem. - 11 Subharmonic Functions and the Dirichlet Problem. - II Exercises. - 0 Review of Complex Numbers. - 1 Elementary Theory of Holomorphic Functions. - 2 Covering Spaces and the Monodromy Theorem. - 3 The Winding Number and the Residue Theorem. - 4 Picard's Theorem. - 5 The Inhomogeneous CauchyRiemann Equation and Runge's Theorem. - 6 Applications of Runge's Theorem. - 7 The Riemann Mapping Theorem and Simple Connectedness in the Plane. - 8 Functions of Several Complex Variables. - 9 Compact Riemann Surfaces. - 10 The Corona Theorem. - 11 Subharmonic Functions and the Dirichlet Problem. - Notes for the exercises. - References for the exercises. Language: English