A book for students and researchers in theoretical computer science, mathematics, physics and engineering. Computer algebra is the name of the technology for manipulating mathematical formulae by computer. The rapid evolution of hardware and software makes it accessible to every scientist and engineer who uses mathematical methods. This book aims to provide an introduction to computer algebra, catering to both the interested beginner and the experienced pure mathematician and computer scientist. The new developments in the second edition give a good comprehensive review, and the book contains references to fundamental papers, and worked examples. In addition to being a general text on the subject, the book includes an appendix describing the use of one particular algebra system REDUCE.