Computer Algebra systems represent a rapidly growing application of computer science to all areas of scientific research and computation. Well-known computer algebra systems such as Maple, Macsyma, Mathematica and REDUCE are now a basic tool on most computers. Underlying these systems are efficient algorithms for various algebraic operations. The field of Computer Algebra, or Algorithmic Algebra, constitute the study of these algorithms and their properties, and represents a rich intersection of theoretical computer science with very classical mathematics. Yap's book focuses on a collection of core problems in this area; in effect, they are the computational versions of the classical Fundamental Problem of Algebra and its derivatives. It attempts to be self-contained in its mathematical development while addressing the algorithmic aspects of problems. General prerequesites for the book, beyond some mathematical sophistication, is a course in modern algebra. A course in the analysis of algorithms would also increase the appreciation of some of the themes on efficiency. The book is intended for a first course in algorithmic algebra (or computer algebra) for advanced undergraduates or beginning graduate students in computer science. Additionally, it will be a useful reference for professionals in this field.