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　　Inrecentyearstherehasbeenenormousactivityinthetheoryofalgebraiccurves．Manylong·standingproblemshavebeensolvedusingthegeneraltechniquesdevelopedinalgebraicgeometryduringthe1950’Sand1960’S．Additionally，unexpectedanddeepconnectionsbetweenalgebraiccurvesanddifferentialequationshavebeenuncovered．a(chǎn)ndtheseinturnshedlightonotherclassicalproblemsincurvetheory．Itseemsfairtosaythatthetheoryofalgebraiccurveslookscompletelyditierentnowfromhowitappeared15yearsago；inparticular，ourcurrentstateofknowledgerepre-sentsasignificantadvancebeyondthelegacyleftbytheclassicalgeometerssuchasNoether，Castelnuovo，Enriques，andSeveri．

　　Thesebooksgiveapresentationofoneofthecentralareasofthisrecentactivity：namely，thestudyoflinearseriesonbothafixedcurve（VolumeI）andonavariablecurverVolumeII）．OurgoaliStogiveacomprehensiveandself-containedaccountoftheextrinsicgeometryofalgebraiccurves，whichinouropinionconstitutesthemaingeometriccoreoftherecentadvancesincurvetheory．Alongthewayweshall，ofcourse，discussappli．cationsofthetheoryoflinearseriestoanumberofclassicaltopics（e…gthegeometryoftheRiemannthetadivisor）aswellastosomeofthecurrentresearchr（e.gtheKodairadimensionofthemodulispaceofcurves）．