We review the construction of the multiparametric quantum group ISO q, r ( N) as a projection from SO q, r ( N + 2) and show that it is a bicovariant bimodule over SO q, r ( N). The universal enveloping algebra U q, r ( iso( N)), characterized as the Hopf algebra of regular functionals on ISO q,r(N), is found as a Hopf subalgebra of U q, r ( so( N + 2)) and is shown to be a bicovariant bimodule over U q, r ( so( N)). An R-matrix formulation of U q, r ( iso( N)) is given and we prove the pairing U q, r ( iso( N)) — ISO q, r ( N)). We analyze the subspaces of U q,r(iso(N)) that define bicovariant differential calculi on ISO q, r ( N).