Evolution Properties of Clusters and AXAF Contributions to understanding Clusters

Our ROSAT survey for distant clusters of galaxies contains the largest solid angle of all ROSAT pointed surveying and thus has sufficient area to test the previously reported cluster evolution. We find significant negative cluster evolution, i.e,, at high redshifts there are fewer luminous clusters than at present. We compare optical cluster properties for the most distant clusters in the ROSAT survey with those measured for nearby clusters. We also present AXAF capabilities and show how AXAF will significantly extend our understanding of cluster properties and their cosmological evolution.