Implications of the study of galaxy clusters and cosmic
large-scale structure on neutrino masses and Dark Matter

Galaxy clusters are sensitive probes of the large-scale
structure of the matter density distribution of the 
Universe and they allow to obtain observational 
constraints of the masses if neutrinos. X-ray 
observations provide currently the best means 
to detect and characterise galaxy clusters. Using
a statistically complete sample of galaxy clusters detected
in the ROSAT All-Sky X-ray Survey, we constrain cosmological
parameters, specifically the matter density and the amplitude
of the large-scale matter density fluctuations. A comparison
of these results with the measurements of cosmic microwave
background anisotropies with the Planck satellite show some
tension, which implies a less pronounced fluctuation
amplitude of nearby large-scale structure as compared to the
predictions based on Planck and a pure LCDM model.
Damping of fluctuations by neutrino Dark Matter provides
a plausible explanation for this discrepancy. We discuss the
constraints on the neutrino mass from these findings and
from other measurements of the nearby large-scale structure 
of the Universe.