Covers the subject of computational group theory (CGT). This book describes the connections between the different aspects of CGT and other areas of computer algebra. It is suitable for graduate students who have some knowledge of group theory and computer algorithms.

This handbook covers the whole subject of computational group theory (CGT) at a level suitable for beginning graduate students who have some knowledge of group theory and computer algorithms. It develops the theory of algorithms in full detail, includes complexity analyses whenever possible, and highlights the connections between the different aspects of CGT and other areas of computer algebra. Several specialist sections provide pointers to the current state of the art in these areas, and all sections include exercises of varying difficulty. For each major collection of algorithms, the book includes a section describing applications both within and outside of group theory.

"This is a book I am very happy to have, both for the choice of content and the quality of exposition. Its subject is a very complete and up-to-date review of computational group theory. ?All together, the book contains of a huge amount of information. ?I think every mathematician will want this book on his shelf."-Mathematics of Computation "It will be an indispensable source for any user in this field." - G. Kowol, in Monatshefte fur Math, 2007, Vol. 151, No. 3