In ℝn (n≥3), we first define a notion of weak solutions to the Keller-Segel system of parabolic-elliptic type in the scaling invariant class Ls((0,T);Lr(ℝn)) for 2∕s+n∕r=2 with n∕2<r<n. Any condition on derivatives of solutions is not required at all. The local existence theorem of weak solutions is established for every initial data in Ln∕2(ℝn). We prove also their uniqueness. As for the marginal case when r=n∕2, we show that if n≥4, then the class C([0,T);Ln∕2(ℝn)) enables us to obtain the only weak solution.