BASIC FACTS IN ALGEBRAIC NUMBER THEORY. Volume 1

This book is a collection of University lecture-notes for : ``Commutative algebra'' and ``Algebraic number theory'' classes. It is a selection of main important notions, and covers the standard basic material in the said topics. Starting at an elementary level, the text peruses very serious aims. The first volume concerns abstract topics namely : Homological Algebra, Profinite groups, as well as chapters containing questions that are still object of research, like local fields with imperfect residue field. The second volume is destined to questions of number theory and commutative Algebra: like Algebraic extensions of fields and integer extensions of rings, Localization and Local fields and some Practical Facts especially a practice determination of some normal extensions of Qp. At the very end, the last part is destined to practical Facts on elementary Algebra and Algebraic number theory with the famous Chinese Remainder Theorem.Since exercises reinforce the reader's grasp of the material. A huge number of exercises, remarks or and examples, that touch the sensitive nerve, are given.