Helffer B., Mohamed A. Asymptotic of the Density of States for the Schr\"odinger Operator with Periodic Electric Potential (131K, LATEX) ABSTRACT. We analyze in this article the spectral properties of the Schr\"odinger operator with periodic potential on L^2(\rz^n). It is proven that the integrated density of states N(\mu) has an asymptotic expansion of the form N(\mu) =a_n \mu^{n/2}+a_{n-2} \mu^{\frac{n-2}{2}}+O(\mu^{(n-3+\epsilon)/2}), for all \epsilon >0. This gives also a proof of the Bethe-Sommerfeld conjecture for n<5.