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

### Famous quotes containing the word theory:

“We have our little *theory* on all human and divine things. Poetry, the workings of genius itself, which, in all times, with one or another meaning, has been called Inspiration, and held to be mysterious and inscrutable, is no longer without its scientific exposition. The building of the lofty rhyme is like any other masonry or bricklaying: we have theories of its rise, height, decline and fall—which latter, it would seem, is now near, among all people.”

—Thomas Carlyle (1795–1881)