Galois Theory is a branch of mathematics that connects field theory and group theory. It studies the symmetries of the roots of polynomial equations, helping to determine whether a given polynomial can be solved using radicals. Named after the mathematician Évariste Galois, this theory provides a framework for understanding the solvability of equations based on the structure of their associated groups. The key idea in Galois Theory is the relationship between a polynomial's roots and the group of permutations of those roots. By analyzing these permutations, mathematicians can classify polynomials as solvable or unsolvable by radicals, leading to important insights in algebra and beyond.