Historical Introduction. Classical Algebra. The Fundamental Theorem of Algebra. Factorization of Polynomials. Field Extensions. Simple Extensions. The Degree of an Extension. Ruler-and-Compass Constructions. The Idea Behind Galois Theory. Normality and Separability. Counting Principles. Field Automorphisms. The Galois Correspondence. A Worked Example. Solubility and Simplicity. Solution by Radicals. Abstract Rings and Fields. Abstract Field Extensions. The General Polynomial. Regular Polygons. Finite Fields. Circle Division. Calculating Galois Groups. Algebraically Closed Fields. Transcendental Numbers. References. Index.