Complex Variables: An Introduction

This text gives an overview of the basic properties of holomorphic functions of one complex variable. Topics studied in this overview include a detailed description of differential forms, homotopy theory and homology theory as the analytic properties of holomorphic functions, the solvability of the inhomogeneous Cauchy-Riemann equation with emphasis on the notation of compact families, the theory of growth of subharmonic functions and an introduction to the theory of sheaves, covering spaces and Riemann surfaces. A number of exercises of differing levels of difficulty have been added.