I. Preliminaries -- 1. Introductory Remarks on Quadratic Forms -- 2. Algebraic Background -- 3. Quadratic Euclidean Rings -- 4. Congruence Classes -- 5. Polynomial Rings -- 6. Dedekind Domains -- 7. Extensions of Dedekind Domains -- 8. Rational and Elliptic Functions -- II. Ideal Structure in Number Fields -- 9. Basis and Discriminant -- 10. Prime Factorization -- 11. Units -- 12. Geometry of Numbers -- 13. Finite Determination of Class Number -- III. Introduction to Class Field Theory -- 14. Quadratic Forms, Rings and Genera -- 15. Ray Class Structure and Fields, Hilbert Class Fields -- 16. Hilbert Sequences -- 17 Discriminant and Conductor -- 18. The Artin Isomorphism -- 19. The Zeta-Function -- Appendices (by Olga Taussky) -- Lectures on Class Field Theory by E. Artin (Gรถttingen 1932) Notes by O. Taussky -- into Connections Between Algebraic Number Theory and Integral Matrices (Appendix by Olga Taussky) -- Subject Matter Index