During December 2000,1 gave a course of ten lectures on Algebraic Number Theory at the University of Kiel in Germany. These lectures were aimed at giving a rapid introduction to some basic aspects of Algebraic Number Theory' with as few prerequisites as possible. I had also hoped to cover some parts of Algebraic Geometry based on the idea, which goes back to Dedekind, that algebraic number fields and algebraic curves are analogous objects. But in the end, I had no time to discuss any Algebraic Geometry. However, I tried to be thorough in regard to the material discussed and most of the proofs were either explained fully or at least sketched during the lectures. These lecture notes are a belated fulfillment of the promise made to the participants of my course and the Kieler Graduiertenkolleg. I hope that they will still be of some use to the participants of my course and other students alike.