I review recent observational progress made in the study of the evolution of the abundance of X-ray galaxy clusters out to large redshifts. The ROSAT Deep Cluster Survey (RDCS) has extended such a work to the faintest fluxes and highest redshifts probed so far in X-ray surveys. A quarter of the spectroscopically identified clusters in the RDCS sample lie at z>0.5. The measured X-ray Luminosity Function (XLF) as a function of redshifts in conjunction with deep cluster number counts reveals that the bulk of the population of galaxy clusters is not evolving significantly since at least z ~= 0.8; mild evolution limited to only the most luminous, presumably most massive systems, remains a possibility.
Large Scale Structure: Tracks and Traces
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