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Number theory --- 512.62 --- Class field theory --- Algebraic number theory --- Fields. Polynomials --- Class field theory. --- 512.62 Fields. Polynomials

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Galois Theory is one of the most beautiful topics in algebra, as both a mathematical theory and as a wonderful history. This is the first book to detail this history. The book covers the basic material of Galois theory and discusses many related topics (Abelian equations, solvable equations of prime degree, and the casus irreducibilis) not mentioned in most standard treatments of Galois theory. It also describes the rich history of Galois theory, including the work of Lagrange, Gauss, Abel, Galois, Jordan, and Kronecker._ Many books on Galois theory are "thin and elegant", aiming for a_sparse but beautiful presentation of the theory._ This book is a "fat" book on Galois theory in an effort to help_readers to understand not only the elegance of the ideas, but also where they came from_and how they relate to other areas of mathematics._

Galois theory --- 512.62 --- Equations, Theory of --- Group theory --- Number theory --- Fields. Polynomials --- Galois theory. --- 512.62 Fields. Polynomials

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Ordered algebraic structures --- Gröbner bases --- Convex polytopes --- 512.62 --- Grobner bases --- Polytopes --- Gröbner basis theory --- Commutative algebra --- Fields. Polynomials --- Convex polytopes. --- Gröbner bases. --- 512.62 Fields. Polynomials --- Gröbner bases

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Ordered algebraic structures --- Algebraic number theory --- Algebraïsche getallentheorie --- Algebraïsche velden --- Fields [Algebraic ] --- Nombres algébriques [Théorie des ] --- 512.62 --- Fields. Polynomials --- Algebraic fields. --- Algebraic number theory. --- 512.62 Fields. Polynomials --- Algebraic fields

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Ordered algebraic structures --- Algèbre universelle. --- Algebra, Universal --- Polynomials --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Algebra, Multiple --- Multiple algebra --- N-way algebra --- Universal algebra --- Algebra, Abstract --- Numbers, Complex --- 512.62 --- #TCPW W2.0 --- #TCPW W2.1 --- 512.62 Fields. Polynomials --- Fields. Polynomials --- Algèbres commutatives --- Algebra, Universal. --- Algèbre universelle --- Algèbres commutatives --- Polynomes