Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms the creation of new paradigms for implementing computational methods the viewing of old techniques from a concrete algorithmic vantage point to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity ranging from category theory graph theory and combinatorics to more classical computational areas such as group theory and number theory. Many of the papers in the book provide a survey of their topic as well as a description of present research. Throughout the variety of mathematical and computational fields represented the emphasis is placed on the common principles and the methods employed. Audience: Students experts and those performing current research in any of the topics mentioned above.