This text, which is also available in HTML and PDF formats at https: //complexanalysis.org, was vetted through six editions with Jones and Bartlett publishing. It provides a comprehensive first course in complex analysis to include many applications in science and engineering. Designed to display the beauty of mathematical thinking, it contains a survey of the intricate and controversial history of the evolution of complex numbers. It is written in a way that allows for flexibility in teaching styles, but does not gloss over theoretical notions. There is an interesting section on the Mandelbrot set, as well as sections dealing with applications in a variety of areas.