Galois theory allows one to reduce certain problems in field theory, especially those related to field extensions, to problems in group theory. For questions about field theory and not Galois theory, use the (field-theory) tag instead. For questions about abstractions of Galois theory, use (galois-connections).
Galois theory is an area of abstract algebra introduced by Evariste Galois. The key point is that it provides a connection between field theory and group theory. We can achieve a greater level of abstraction by a correspondence between two partially ordered sets called Galois connections.