Let Sd = k[Xo,..., Xn]d be the k-vector space of homogeneous polynomials of degree d in (n + I)-variables Xo,... ,Xn and the zero polynomial over an algebraically closed field k of characteristic 0. In this paper, the authors show that the birational maps of degree d of the projective space Pnk form a locally closed subvariety of the projective space P(Sn+1,d) associated with Sn+1,d, denoted Crd(n). The authors also prove the existence of the quotient variety PGL(n + 1)\Crd(n) that parametrize all the birational maps of degree d of P(Sn+1,d) modulo the projective linear group PGL(n + 1) on the left.