Reciprocity Laws II. From Kummer to Hilbert

12. Quadratic Reciprocity in Number Fields (Nov. 19, 2005)

Quadratic reciprocity laws in quadratic number fields

13. Eisenstein's Conjecture

Eisenstein's 'derivation' of the l-th power reciprocity law in cyclotomic fields

14. Analytic Techniques

15. Genus Theory

16. Kummer's Reciprocity Law

17. Hilbert's Reciprocity Law

18. Hecke's Gauss Sums and Quadratic Reciprocity

19. Theta Functions

20. Norm Residues

21. Hilbert Class Field Theory

22. Quaternion Algebras

23. Quadratic Function Fields

I hope to have preliminary versions of these chapters up here until the end of 2005. Comments are more than welcome. Please let me know about mistakes, typos, omissions, ...