This book brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike. The Second Edition features new exercises and an updated bibliography. A new discussion provides a different method for computing the Galois group of a quartic polynomial. Chapter coverage includes: cubic equations; symmetric polynomials; roots of polynomials; extension fields; normal and separable extensions; the Galois group; the Galois correspondence; solvability by radical; cyclotomic extensions; geometric constructions; finite field; computing Galois groups; solvable permutation groups; the Lemniscate; and an introduction to abstract algebra.