The primary textbook for the course will be Swinnerton-Dyer's A Brief Guide to Algebraic Number Theory. You should buy this book (it only costs $27). I'm also creating a list of mistakes and typos in the book (if you find one not on the list, send me an email).
I like the following, which are relevant to the course:
These books are also good:
Any time I mention a paper in class I will try to add a link to it here. These are in alphabetical order by author.