Classical algebra -- Fundamental theorem of algebra -- Factorisation of polynomials -- Field extensions -- Simple extensions -- Degree of an extension -- Ruler-and-compass constructions -- Idea behind Galois theory -- Normality and separability -- Counting principles -- Field automorphisms -- Galois correspondence -- Worked example -- Solubility and simplicity -- Solution by radicals -- Abstract rings and fields -- Abstract field extensions -- General polynomial equation -- Finite fields -- Regular polygons -- Circle division -- Calculating Galois groups -- Algebraically closed fields -- Transcendental numbers -- What did Galois do or know?