如果很多笔记来源于同一本书，那么这里只插入链接，将具体内容放在相关书籍的博客中。
下述文字来源于Franz Lemmermeyer & Norbert Schappacher的文章 Introduction to the English Edition of Hilbert's Zahlbericht（September 11, 2003）
- 当代数论著作为何多避免 genus theory：（目前还不明白，以后学了再回顾）
Working up towards his general reciprocity law, Kummer's central achievement was to build up genus theory for Kummer extensions of (mathbb{Q}(zeta_ell)). Accordingly, genus theory plays a very important role in the Zahlbericht. This is quite different from what we are used to nowadays: for instance, the books by Samuel or Neukirch cited above never even mention genus theory. One reason for its disappearance in our time was Chevalley's introduction of ideles, which made it possible to develop class field theory without going through the notorious index calculus of the ideal-theoretic approach via genus theory.