This book is in two parts. The first is intended to serve as a basis for a first course on complex function theory for both undergraduate and graduate
students. It is not expected that the whole of Part One will be " covered " in a
semester. Experience and realism would say that the larger part of the first
seven chapters is manageable. Part One can constitute a semester course when
an adequate level of maturity is available. Chapter IX, the final chapter of
Part One, culminates in the proof of the prime number theorem of Hadamard
and de la Vallee Poussin—a particularly handsome application of topics
treated in earlier chapters. I dare say that a syllabus consisting of the
material presented in Part One forms a reasonable and, in fact, mathematically
appealing program that can serve as a basis for the requirements in complex
function theory for all doctoral candidates in mathematics at present.