  We present results of analysis of physical conditions (number density,
intensity of UV field, kinetic temperature) in the cold H$_2$-bearing
interstellar medium of local and high redshift galaxies. Our measurements based
on the fit to the observed population of H$_2$ rotational levels and CI
fine-structure levels with the help of grids of numerical models calculated
with the PDR Meudon code. A joint analysis of low H$_2$ rotational levels and
CI fine-structure levels allows to break the degeneracy in the
$I_{UV}-n_{\rm{H}}$ plane and provides significantly tighter constraints on the
number density and intensity of UV field. Using archive data from the VLT/UVES,
KECK/HIRES, HST/STIS and FUSE telescopes we selected 12 high redshift damped
Ly$\alpha$ systems (DLAs) in quasar spectra and 14 H$_2$ absorption systems
along the lines of sight towards stars in the Milky-Way and the Magellanic
Clouds galaxies. These systems have strong H$_2$ components with the column
density $\log N({\rm{H_2}})/{\rm{cm}}^{-2}>18$ and associated CI absorptions.
We find that H$_2$-bearing medium in high redshift DLAs and in local galaxies
has similar values of the kinetic temperatures $T_{\rm{kin}}\sim100$K and
number density $10-500$ cm$^{-3}$. However, the intensity of incident UV
radiation in DLAs is varied in the wide range ($0.1-100$ units of Mathis
field), while it is $\sim0.1-3$ units of Mathis field for H$_2$ systems in
Milky-Way and LMC and SMC galaxies. The large dispersion of measured UV flux in
DLAs is probably a consequence that DLA sample probes the galaxies selected
from the overall galaxy population at high-z and therefore corresponds to the
wide range of the physical conditions.
