This book (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton's, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent's method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled "A Handbook of Methods for Polynomial Root-finding". This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. - First comprehensive treatment of Root-Finding in several decades.- Gives description of high-grade software and where it can be down-loaded.- Very up-to-date in mid-2006; long chapter on matrix methods.- Includes Parallel methods, errors where appropriate.- Invaluable for research or graduate course.