  In this paper we study the shear viscosity temperature dependence of
$SU(3)$--gluodynamics within lattice simulation. To do so, we measure the
correlation functions of energy-momentum tensor in the range of temperatures
$T/T_c\in [0.9, 1.5]$. To extract the values of shear viscosity we used two
approaches. The first one is to fit the lattice data with some physically
motivated ansatz for the spectral function with unknown parameters and then
determine shear viscosity. The second approach is to apply the Backus-Gilbert
method which allows to extract shear viscosity from the lattice data
nonparametrically. The results obtained within both approaches agree with each
other. Our results allow us to conclude that within the temperature range
$T/T_c \in [0.9, 1.5]$ SU(3)--gluodynamics reveals the properties of a strongly
interacting system, which cannot be described perturbatively, and has the ratio
$\eta/s$ close to the value ${1}/{4\pi}$ in $N = 4$ Supersymmetric Yang-Mills
theory.
