In mathematics, more specifically in abstract algebra, **Galois theory**, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood.

Originally Galois used permutation groups to describe how the various roots of a given polynomial equation are related to each other. The modern approach to Galois theory, developed by Richard Dedekind, Leopold Kronecker and Emil Artin, among others, involves studying automorphisms of field extensions.

Further abstraction of Galois theory is achieved by the theory of Galois connections.

Read more about Galois Theory: Application To Classical Problems, History, Permutation Group Approach To Galois Theory, Modern Approach By Field Theory, Solvable Groups and Solution By Radicals, Inverse Galois Problem

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