The bock provides an introduction to complex analysis for students with some familiarity with complex numbers hum high school. The book consists of three parts. The first part constitutes the basic tore of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics as the argument principle, the Schwarz lemma and hyperbolic geometry, the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing Ph.D.-qualifying exams in complex analysis. Topics selected include Julie sets and the Mandelbrot set, Dirichlet caries and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries-spherical, Euclidean, and hyperbolic-ore stressed. Exercises range hum the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, particularly the Interuniversity Summer School at Perugia (Italy), and also UCLA, Brown University, Valencia (Spain), and La Plate (Argentina).