The usual reference here is Serre's *Algebraic Groups and Class Fields*. But it still felt to me like there was a lot of magic left over after I read this.

We had an [earlier question along similar lines][1] with many good answers. I remember really liking [David Ben Zvi's lecture][2], but wishing that some one would write up the "decategorification" to get from the categorical statements in Ben Zvi's talk to concrete reciprocity laws.

Even more [old answers here][3].


  [1]: https://mathoverflow.net/questions/73054
  [2]: https://www.msri.org/workshops/137/schedules/687
  [3]: https://mathoverflow.net/questions/100798