Theimplicitfunctiontheoremis.alongwithitsclosecousintheinversefunc-tiontheorem，oneofthemostimportant，andoneoftheoldest，paradigmsinmodcrnmathemarics.OnecanseethegermoftheideafortheimplicirfunctiontheoreminthewritingsofIsaacNewton（1642-1727），andGottfriedLeib-niz's（1646-1716）workcxplicittycontainsaninstanceofimplicitdifferentiation.　　WhilcJosephLouisLagrange（1736-1813）foundatheorcmthatisessentiallyaversionoftheinversefunctiontheorem，icwasAugustin-LouisCauchy（1789-1857）whoapproachedtheimplicitfunctiontheoremwithmathematicalrigoranditishewhoisgencrallyacknowledgcdasthediscovcrerofthetheorem.InChap-ter2，wewillgivedetailsofthecontributionsofNewton，Lagrange，andCauchytothedevelopmentoftheimplicitfunctiontheorem.