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The mass function of galaxy clusters is a sensitive tracer of thegravitational evolution of the cosmic large-scale structure and serves as animportant census of the fraction of matter bound in large structures. We obtainthe mass function by fitting the observed cluster X-ray luminosity distributionfrom the REFLEX galaxy cluster survey to models of cosmological structureformation. We marginalise over uncertainties in the cosmological parameters aswell as those of the relevant galaxy cluster scaling relations. The massfunction is determined with an uncertainty less than 10% in the mass range 3 x10^12 to 5 x 10^14 M$_\odot$. For the cumulative mass function we find a slopeat the low mass end consistent with a value of -1, while the mass rich endcut-off is milder than a Schechter function with an exponential term exp($-M^\delta$) with $\delta$ smaller than 1. Changing the Hubble parameter in therange $H_0 = 67 - 73 km s^-1 Mpc^{-1}$ or allowing the total neutrino mass tohave a value between 0 - 0.4 eV causes variations less than the uncertainties.We estimate the fraction of mass locked up in galaxy clusters: about 4.4% ofthe matter in the Universe is bound in clusters (inside $r_200$) with a masslarger than 10^14 M$_\odot$ and 14% to clusters and groups with a mass largerthan 10^13 M$_\odot$ at the present Universe. We also discuss the evolution ofthe galaxy cluster population with redshift. Our results imply that there ishardly any clusters with a mass > 10^15 M$_\odot$ above a redshift of z = 1.

The extended ROSAT-ESO Flux-Limited X-ray Galaxy Cluster Survey (REFLEX II) VII The Mass Function of Galaxy Clusters