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We present a new, objectively selected, sample of galaxy overdensitiesdetected in the Hubble Space Telescope Medium Deep Survey. Theseclusters/groups were found using an automated procedure which involvedsearching for statistically significant galaxy overdensities. The contrast ofthe clusters against the field galaxy population is increased whenmorphological data is used to search around bulge-dominated galaxies. In total,we present 92 overdensities above a probability threshold of 99.5%. We show,via extensive Monte Carlo simulations, that at least 60% of these overdensitiesare likely to be real clusters and groups and not random line-of-sightsuperpositions of galaxies. For each overdensity in the MDS cluster sample, weprovide a richness and the average of the bulge-to-total ratio of galaxieswithin each system. This MDS cluster sample potentially contains some of themost distant clusters/groups ever detected, with about 25% of the overdensitieshaving estimated redshifts z > 0.9. We have made this sample publicly availableto facilitate spectroscopic confirmation of these clusters and help moredetailed studies of cluster and galaxy evolution.  We also report the serendipitous discovery of a new cluster close on the skyto the rich optical cluster CLl0016+16 at z=0.546. This new overdensity, HST001831+16208, may be coincident with both an X-ray source and a radio source.HST 001831+16208 is the third cluster/group discovered near to CL0016+16 andappears to strengthen the claims of Connolly et al. (1996) of superclusteringat high redshift.Comment: 25 pages including 7 figures and 9 tables. AJ Vol. 116, No.

The [ITAL]Hubble[/ITAL] [ITAL]Space[/ITAL] [ITAL]Telescope[/ITAL] Medium Deep Survey Cluster Sample: Methodology and Data