Constructibility with Ruler and Compass -- Algebraic Extensions -- Simple Extensions -- Fundamentals of Divisibility -- Prime Factorization in Polynomial Rings. Gauss's Theorem -- Polynomial Splitting Fields -- Separable Extensions -- Galois Extensions -- Finite Fields, Cyclic Groups and Roots of Unity -- Group Actions -- Applications of Galois Theory to Cyclotomic Fields -- Further Steps into Galois Theory -- Norm and Trace -- Binomial Equations -- Solvability of Equations -- Integral Ring Extensions with Applications to Galois Theory -- The Transcendence of -- Fundamentals of Transcendental Field Extensions -- Hilbert's Nullstellensatz