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Consider an oriented compact surface F of positive genus, possibly with boundary, and a finite set P of punctures in the interior of F, and define the punctured mapping class group of F relatively to P to be the group of isotopy classes of orientation-preserving homeomorphisms h: F-->F which pointwise fix the boundary of F and such that h(P) = P. In this paper, we calculate presentations for all punctured mapping class groups. More precisely, we show that these groups are isomorphic withdoi:10.2140/agt.2001.1.73 fatcat:jvxg3bp44bcmlpdxfpc7k2gpu4