THIS BOOK: WHY DOES IT MATTER? This book leads essentially with quaternions and functions of quaternions. Roughly speaking, hypercomplex may be considered as a living subject in the field of Mathematical Analysis, in the sense that a systematical and unifying approach for dealing with them is still missing.In this book we will try to fill that gap. Growing out of a course designed to teach Complex Analysis to honors- level undergraduates of Mathematics and Applied Mathematics at the UNESP (São Paulo State University), this Book is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with Complex Analysis. This book covers a broad variety of topics ranging from a comprehensive overview on the history of quaternions, and a consistente foundation for series, derivation, and integration of hypercomplex., with an exposure of a Cauchy like Theorem. [...]