Bewersdorff, J÷rg. Galois theory for beginners: a historical perspective, tr. by David Kramer. American Mathematical Society, 2006. 180 p. index afp (Stundent mathematical library, 35) ISBN 0821838172 pbk, $ 35.00

Without doubt, Galois theory is one of the crowning achievements of the abstract point of view in algebra. These days, the subject is typically presented in its modern and highly destilled form, without strong connections to its roots in the theory of equations. As a result, it can be difficult to appreciate the degree to which abstract apppoach grew from the very concrete (and clever) calculations for more than a millennium's worth of mathematicians: al-Khwarizmi, Viete, Tartaglia, Cardano, Lagrange, Abel, and, of course Galois, just to name a few. Bewersdorff takes up the challenge of demonstrating how the progression from elementary manipulations to group- and field-theoretic computations is a natural one; moreover, he attemps to do so with very little by way of mathematical prerequisites (in particular, he assumes no background in modern algebra). For those with minimal exposure to undergraduate mathematics, the book would make some formidable reading. However, as a companion text to a first course in field and Galois theory, it provides excellent historical and mathematical context, and well-considered and specific examples that serve as a welcome counterpoint to general algebraic structures and theorems. Summing up: Recommended. Lower-division undergraduate through graduate students. -- S.J. Colley, Oberlin College

CHOICE, Current Reviews for academic libraries, 45 (Sept. 2007 No. 01), 45-0324