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I have studied some basic algebraic number theory, including Dedekind theory, valuation theory, and a little local fields. Now I am thinking to study more and deeper, and hoping to study class field theory, so please help me which book should I choose?

The teacher told me that I should read Lang's or Neukirch's, but I don't know which is better and to choose, or if there is a better one?

Thanks in advance.

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  • $\begingroup$ Not an expert, but I thought I'd add a perhaps non-standard suggestion as a comment: Fermat's Last Theorem, by Edwards, is a historical account of the birth of the algebraic tools involved in attacking FLT, including I believe the ideal class group (related to class field theory?). To be clear, it is an algebraic number theory textbook, not just a history book. $\endgroup$ – Jack M Jun 10 '17 at 14:18
  • $\begingroup$ What books have you already read, if at least partially? $\endgroup$ – Robert Soupe Jun 11 '17 at 22:59
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Don't know about your books, but Artin's book is thought to be a good preparation.

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There is also Weil's Basic Number Theory, Cassels-Fröhlich Algebraic Number Theory, Serre's Local Fields and the lecture notes http://jmilne.org/math/CourseNotes/index.html of James Milne.

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