The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers,including much more material, e.g. the class field theory on which I make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collection of papers from the Brighton Symposium (edited by Cassels-Frohlich),the Artin-Tate notes on class field theory, Well's book on Basic Number Theory, Borevich-Shafarevich's Number Theory, and also older books like those of Weber, Hasse, Hecke, and HUbert's Zahlbericht. It seems that over the years, everything that has been done has proved useful, theoretically or as examples, for the further development of the theory. Old,and seemingly isolated special cases have continuously acquired renewedsignificance, often after half a century or more.