Class Field Theory
by J. S. Milne
Number of pages: 287
Class field theory describes the abelian extensions of a local or global field in terms of the arithmetic of the field itself. These notes contain an exposition of abelian class field theory using the algebraic/cohomological approach of Chevalley and Artin and Tate.
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by M. Kneser - Tata Institute of Fundamental Research
The main result is the Hasse principle for the one-dimensional Galois cohomology of simply connected classical groups over number fields. For most groups, this result is closely related to other types of Hasse principle.
by George Ballard Mathews - Cambridge University Press
This book is intended to give an account of the theory of equations according to the ideas of Galois. This method analyzes, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation.
by J. S. Milne
A concise treatment of Galois theory and the theory of fields, including transcendence degrees and infinite Galois extensions. Contents: Basic definitions and results; Splitting fields; The fundamental theorem of Galois theory; etc.
by Miles Reid - University of Warwick
The author discusses the problem of solutions of polynomial equations both in explicit terms and in terms of abstract algebraic structures. The course demonstrates the tools of abstract algebra as applied to a meaningful problem.