Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!" --Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel's theory of Abelian equations, casus irreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including: * The contributions of Lagrange, Galois, and Kronecker * How to compute Galois groups * Galois's results about irreducible polynomials of prime or prime-squared degree * Abel's theorem about geometric constructions on the lemniscates * Galois groups of quartic polynomials in all characteristics Throughout the book, intriguing Mathematical Notes and Historical Notes sections clarify the discussed ideas