X-ray Cluster Cosmology

Formation of dark matter halos is sensitive to the expansion rate of the Universe and to the growth of structures under gravitational collapse. Virialization of halos heats the gaseous intra-cluster medium to high temperatures, leading to copious emission of photons at X-ray wavelengths. We summarize the progress of X-ray surveys in determining cosmology using galaxy clusters. We review recent cosmological results based on cluster volume abundance, clustering, standard candles, extreme object statistics, and present relevant theoretical considerations. We discuss clusters as gravitation theory probes and present an outlook on future developments.