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In the present paper we construct all typical finite-dimensionalrepresentations of the quantum Lie superalgebra $U_{q}[gl(2/2)]$ at genericdeformation parameter $q$. As in the non-deformed case the finite-dimensional$U_{q}[gl(2/2)]$-module $W^{q}$ obtained is irreducible and can be decomposedinto finite-dimensional irreducible $U_{q}[gl(2)\oplus gl(2)]$-submodules$V^{q}_{k}$Comment: published version. Some formulae are rewritten in more compact for

Finite-dimensional representations of the quantum superalgebra U q[gl(2/2)]. I. Typical representations at generic q