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.