Complex Analysis

Targeted at upper division undergraduates and PhD candidates, this introduction to complex analysis covers essential topics like Julia and Mandelbrot sets, Dirichlet series, and the uniformization theorem for Riemann surfaces. The text emphasizes the three geometries: spherical, Euclidean, and hyperbolic. With sixteen chapters, it includes a range of exercises from simple to challenging, ensuring comprehensive preparation for qualifying exams. The material is drawn from the author's extensive teaching experience at various prestigious universities worldwide.