Thisbookisbasedonone-semestercoursesgivenatHarvardin1984,atBrownin1985,andatHarvardin1988.Itisintendedtobe,asthetitlesuggests,afirstintroductiontothesubject.Evenso,afewwordsareinorderaboutthepurposesofthebook.Algebraicgeometryhasdevelopedtremendouslyoverthelastcentury.Duringthe19thcentury,thesubjectwaspracticedonarelativelyconcrete,down-to-earthlevel;themainobjectsofstudywereprojectivevarieties,andthetechniquesforthemostpartweregroundedingeometricconstructions.ThisapproachflourishedduringthemiddleofthecenturyandreacheditsculminationintheworkoftheItalianschoolaroundtheendofthe19thandthebeginningofthe20thcenturies.Ultimately,thesubjectwaspushedbeyondthelimitsofitsfoundations:bytheendofitsperiodtheItalianschoolhadprogressedtothepointwherethelanguageandtechniquesofthesubjectcouldnolongerservetoexpressorcarryouttheideasofitsbestpractitioners.