Introduction

Galois theory is a branch of abstract algebra that studies the symmetries of algebraic equations. It provides a deep connection between field theory and group theory, revealing the hidden structure behind the solutions of polynomial equations. The theory is named after Évariste Galois, a French mathematician who made significant contributions to the field before his untimely death at the age of 20.

intro_galois_theory

Contents

Symmetric Polynomials and Splitting Fields
Fixed Fields and Galois Extensions
Cubic and Quartic Equations
Roots of Unity
Kummer Extensions and Solvability

Other Resources

Tom Leinster, Galois Theory
Math Visualized, Galois Theory Explained Simply