In mathematics, Galois theory is a branch of abstract algebra.

At the most basic level, it uses permutation groups to describe how the various roots of a given polynomial equation are related to each other. This was the original point of view of Évariste Galois.

The modern approach to Galois theory, developed by Richard Dedekind, Leopold Kronecker and Emil Artin, among others, involves studying automorphisms of field extensions.

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