Galois theory is a branch of mathematics that connects field theory and group theory. It studies the symmetries of the roots of polynomial equations, providing a way to understand when these roots can be expressed using radicals. Named after the mathematician Évariste Galois, this theory helps determine the solvability of polynomial equations by analyzing their associated Galois groups. The main idea of Galois theory is to relate the properties of a polynomial to the structure of its Galois group, which consists of permutations of the roots. This relationship allows mathematicians to classify polynomials and understand their solutions, revealing deep connections between algebra and geometry.