  Galois theory is developed using elementary polynomial and group algebra. The
method follows closely the original prescription of Galois, and has the benefit
of making the theory accessible to a wide audience. The theory is illustrated
by a solution in radicals of lower degree polynomials, and the standard result
of the insolubility in radicals of the general quintic and above. This is
augmented by the presentation of a general solution in radicals for all
polynomials when such exist, and illustrated with specific cases. A method for
computing the Galois group and establishing whether a radical solution exists
is also presented.
