Complexgeometryisahighlyattractivebranchofmodernmathematicsthathaswitnessedmanyyearsofactiveandsuccessfulresearchandthathasre-centlyobtainednewimpetusfromphysicistsinterestinquestionsrelatedtomirrorsymmetry.Duetoitsinteractionswithvariousotherfields(differential,algebraic,andarithmeticgeometry,butalsostringtheoryandconformalfieldtheory),ithasbecomeanareawithmanyfacets.Also,thereareanumberofchallengingopenproblemswhichcontributetothesubjectsattraction.ThemostfamousamongthemistheHodgeconjecture,oneofthesevenone-milliondollarmillenniumproblemsoftheClayMathematicsInstitute.So,itseemslikelytatthisareawillfascinatenewgenerationsformanyyearstocome.