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Notes on class field theory

These are notes on class field theory that I wrote for myself to help understand the subject. If you find them useful in any way at all, that's great! I have attempted to be as self-contained beyond elementary algebra, and in particular the basic facts about algebraic number theory are included. Proofs are sometimes sketched, and they are incomplete in places. If you find a mistake, I shall appreciate it if you email me at amathew@college.harvard.edu. Notes: As of today (June 21, 2010), the notes are a mess. There are many gaps in " Chapter 0, " such as a lack of mention of how the absolute value and prime ideal approach connect to each other, and even mention of Galois operation on ideals. The notes were culled from mostly disjointed and highly irregular blog posts on algebraic number theory, and many of them still retain vestigial features from their evolutionary past.