Swallow (mathematics, Davidson College) works from the assumption his readers are undergraduates who have completed a first course in abstract algebra in this exploration-based approach to Galois theory. In his text he covers algebraic numbers, field extensions, minimal polynomials, multiply generated fields, and the Galois correspondence, closing with such classical topics as binomial equations and solvability in radicals. He also gives students with access to Maple or Mathematica the opportunity to work with finite extensions of the rational numbers. Swallow includes exercises and an historical note.