We report some new results obtained jointly with F. Gotze in cite{GT:2014}, cite{GT:2014a}. We obtain the non-improvable estimates of the rate of convergence of an expected spectral distribution function of Wigner random matrix to the semi-circular law under moment restrictions on the distributions of matrix entries. We prove as well the optimal (up to power of logarithmic factor) bounds of $L_p$-norm of Kolmogorov distance between an empirical spectral distribution function of Wigner random matrix and the semi-circular law under the same assumption about matrix entries distribution. References {GT:2014} Gotze, F.; Tikhomirov, A. N. On the optimal bounds of the rate of convergence of the expected spectral distribution functions to the semi-circle law. Preprint. 2014, available on http://arxiv.org/abs/1405.7820. {GT:2014a} Gotze, F.; Tikhomirov, A. N. Rate of Convergence of the Empirical Spectral Distribution Function to the Semi-Circular Law. Preprint. 2014, available on http://arxiv.org/abs/:1407.2780