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A review of the multiparametric linear quantum group GL_qr(N), its realforms, its dual algebra U(gl_qr(N)) and its bicovariant differential calculusis given in the first part of the paper.  We then construct the (multiparametric) linear inhomogeneous quantum groupIGL_qr(N) as a projection from GL_qr(N+1), or equivalently, as a quotient ofGL_qr(N+1) with respect to a suitable Hopf algebra ideal.  A bicovariant differential calculus on IGL_qr(N) is explicitly obtained as aprojection from the one on GL_qr(N+1). Our procedure unifies in a singlestructure the quantum plane coordinates and the q-group matrix elements T^a_b,and allows to deduce without effort the differential calculus on the q-planeIGL_qr(N) / GL_qr(N).  The general theory is illustrated on the example of IGL_qr(2).Comment: 38 page

INHOMOGENEOUS QUANTUM GROUPS IGLq,r(N): UNIVERSAL ENVELOPING ALGEBRA AND DIFFERENTIAL CALCULUS

INHOMOGENEOUS QUANTUM GROUPS IGL_q,r(N): UNIVERSAL ENVELOPING ALGEBRA AND DIFFERENTIAL CALCULUS