Galois Theory Book

	Preface to the Second Edition
	Preface to the First Edition
	To the Reader
	Symmetry	1
	Rings	7
	Domains and Fields	13
	Homomorphisms and Ideals	17
	Quotient Rings	21
	Polynomial Rings over Fields	24
	Prime Ideals and Maximal Ideals	31
	Irreducible Polynomials	38
	Classical Formulas	44
	Splitting Fields	50
	The Galois Group	59
	Roots of Unity	63
	Solvability by Radicals	71
	Independence of Characters	76
	Galois Extensions	79
	The Fundamental Theorem of Galois Theory	83
	Applications	85
	Galois's Great Theorem	90
	Discriminants	95
	Galois Groups of Quadratics, Cubics, and Quartics	100
	Epilogue	107
App. A	Group Theory Dictionary	109
App. B	Group Theory Used in the Text	112
App. C	Ruler-Compass Constructions	129
App. D	Old-fashioned Galois Theory	138
	References	151
	Index	153