A Classical Invitation to Algebraic Numbers and Class Fields: Universitext

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 (Göttingen 1932) Notes by O. Taussky.- into Connections Between Algebraic Number Theory and Integral Matrices (Appendix by Olga Taussky).- Subject Matter Index.