This thoroughly revised and updated version of the popular textbook on abstract algebra introduces students to easily understood problems and concepts. John Humphreys and Mike Prest include many examples and exercises throughout the book to make it more appealing to students and instructors. The second edition features new sections on mathematical reasoning and polynomials. In addition, three chapters have been completely rewritten and all others have been updated. First Edition Pb (1990): 0-521-35938-4

The study of the symmetric groups forms one of the basic building blocks of modern group theory. This book is the first completely detailed and self-contained presentation of the wealth of information now known on the projective representations of the symmetric and alternating groups. Prerequisites are a basic familiarity with the elementary theory of linear representations and a modest background in modern algebra. The authors have taken pains to ensure that all the relevant algebraic and combinatoric tools are clearly explained in such a way as to make the book suitable for graduate students and research workers. After the pioneering work of Issai Schur, little progress was made for half a century on projective representations, despite considerable activity on the related topic of linear representations. However, in the last twenty years important new advances have spurred further research. This book develops both the early theory of Schur and then describes the key advances that the subject has seen since then. In particular the theory of Q-functions and skew Q-functions is extensively covered which is central to the development of the subject.