Hailed as a milestone in the development of modern algebra, this classic exposition of the theory of groups is well within the range of graduate students. Its particular value lies in its attention to practical applications: the theory of the solvability of equations, theory of differential equations, complex number systems, and the foundations of geometry, where Euclidean or parabolic geometry, elliptic geometry, and hyperbolic geometry can be completely characterized by groups. The first of the two-part treatment consists of an extensive presentation of the theory of Galois Fields, with a wealth of examples and theorems; the second part features a discussion of linear groups in a Galois Field, with a survey of the known simple groups of finite composite order. 1901 ed.