Here is a work that breaks with tradition and organizes the basic
material of complex analysis in a unique manner. The authors' aim is to
present a precise and concise treatment of those parts of complex
analysis that should be familiar to every research mathematician. They
follow a path in the tradition of Ahlfors and Bers by dedicating the
book to a very precise goal: the statement and proof of the Fundamental
Theorem for functions of one complex variable. The first part of the
book is a study of the many equivalent ways of understanding the concept
of analyticity, and move on to offer a leisurely exploration of
interesting consequences and applications. The book covers most, if not
all, of the material contained in Bers's courses on first year complex
analysis. In addition, topics of current interest such as zeros of
holomorphic functions and the connection between hyperbolic geometry and
complex analysis are explored. Readers should have had undergraduate
courses in advanced calculus, linear algebra, and some abstract algebra.