Galois theory is considered one of the most difficult topics in undergraduate Mathematics. In this book polynomials have been explained to be solvable by radicals , plotting their roots in a complex plane as polygons. Some automorphisms of the roots (permutations ) fix the polygon and some do not. They form Galois group for the polynomial . It is made evident from root polygon some automorphisms , rigid rotations and reflections that fix the figure guarantee solvability if the Galois group is cyclic or product of cyclic groups, i,e., abelian. Next the reader is led to some bare basics of group theory , field theory and vector spaces . The problem of polynomial is translated to problem of fields and groups in turn and solvability is extended from abelian groups to Normal subgroups forming a subnormal series. Also through commutator subgroups and derived series of finite length.