Artin's approach begins with his analysis of groups, including the concept of a group itself and the phenomena of subgroups. He describes rings and fields, including linear equations in a field and vector spaces, polynomials over a field, factorization into primes, ideals and the greatest common divisor, solution of the general equation of nth degree, residual classes, extension fields, and isomorphisms. He explains Galois theory, including such topics as splitting fields and their automorphisms, the characteristics of a field, derivation of a polynomial (multiple roots), the degree of an extension field, group characters, fundamental theorems and finite fields, then moves to polynomials with integral coefficients, including irreducibility and primitive roots of unity, and the theory of equations, including ruler and compass constructions, and the theorems of Steinitz and Abel. This classic 1947 treatment, formerly titled Modern Higher Algebra Galois Theory, has been annotated by Albert A. Blank. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)