Here are some slides I made in Beamer for a presentation I did for the Directed Reading Program with Ramanujan Srihari in Spring 2024 at UCSD. They are essentially Chapter 3 of Neukirch’s Algebraic Number Theory. The motivation here is to reformulate much of the theory developed in the first 2 chapters via ideal theory into the language of geometry, reinforcing the idea that ``number theory is part of geometry’’ Neukirch mentions a handful of times in the book. In any case, this presentation was meant to fit into a 15 minute time frame, so it doesn’t go too much into detail with the proofs. Hopefully, the presentation in the slides is largely issue-free!