This book is the second of a two volume work which attempts to give a broad introduction to the subject of abstract algebra. It assumes no previous knowledge of this work but does expect a fair amount of mathematical sophistication. Thus it is not intended to be used as a textbook at an elementary level in schools, as part of one of the ‘modern mathematics’ courses, but is aimed rather at a fairly intelligent sixth-former, who has been brought up on either traditional or modern syllabuses and who wishes to know something more about modern algebra, for example as a preparation for university work. This second volume in particular should be found useful by undergraduates, as giving a broad background before a study in more depth is undertaken, and it does in fact cover a great deal of work usually included in university first degree courses, though not all such work. Teachers in schools and students in teacher training colleges who wish to learn some abstract algebra as an aid and background to their teaching should also find parts of both volumes interesting and useful. Numerous books on the subject have been and are being written, but these are usually either too advanced, with a lack of motivation, for the beginner, or are written at a far less sophisticated level, for younger pupils. It is still not easy to find many which start from the beginning and lead up to substantial and important ideas gradually and in a fairly elementary manner.