ThepresentbookgivesanexpositionoftheclassicalbasicalgebraicandanalyticnumbertheoryandsupersedesmyAlgebraicNumbers,includingmuchmorematerial,e.g.theclassfieldtheoryonwhichImakefurthercommentsattheappropriateplacelater.Fordifferentpointsofview,thereaderisencouragedtoreadthecollectionofpapersfromtheBrightonSymposium(editedbyCassels-Frohlich),theArtin-Tatenotesonclassfieldtheory,WellsbookonBasicNumberTheory,Borevich-ShafarevichsNumberTheory,andalsoolderbookslikethoseofWeber,Hasse,Hecke,andHUbertsZahlbericht.Itseemsthatovertheyears,everythingthathasbeendonehasproveduseful,theoreticallyorasexamples,forthefurtherdevelopmentofthetheory.Old,andseeminglyisolatedspecialcaseshavecontinuouslyacquiredrenewedsignificance,oftenafterhalfacenturyormore.