This is a series of posts on algebraic number theory which builds upon my previous series on field theory. The goals are mostly the same: to give the interested reader with only a modest background in mathematics a first “feel” of the subject, and perhaps to motivate further study. I have tried to also keep the same style of exposition, but the pace will be somewhat faster, and might be difficult to follow for the reader who has merely read my previous series and not otherwise done a lot of work with the basic objects of algebra (groups, rings, fields, polynomials).

For the (relative) beginner wishing to study algebraic number theory I warmly recommend Marcus’s book (and indeed much of what I will write in this series will be based on it). At the beginning, it requires only a very modest background in abstract algebra (having studied everything in Fraleigh’s book will more than suffice), and the level rises progressively, which makes it possible to study it in parallel with a more advanced course in abstract algebra.

The posts are as follows:

1 – **R** vs. **Q** and number fields

2 – Rings

3 – Unique factorisation

4 – Cyclotomic fields