This work offers a treatment of fundamental methods and algorithms in computational group theory (CGT) at a level accessible to advanced undergraduates. It develops the theory of algorithms in detail and highlights the connections between the different aspects of CGT and other areas of computer algebra. While acknowledging the importance of the complexity analysis of CGT algorithms, the book's primary focus is on algorithms that perform well in practice rather than on those with the best theoretical complexity. Applications of algorithms demonstrate how CGT fits into the wider world of mathematics and science