We present the Bright SHARC (Serendipitous High-Redshift Archival ROSAT Clu
ster) Survey, which is an objective search for serendipitously detected ext
ended X-ray sources in 460 deep ROSAT PSPC pointings. The Bright SHARC Surv
ey covers an area of 178.6 deg(2) and has yielded 374 extended sources. We
discuss the X-ray data reduction, the candidate selection and present resul
ts from our ongoing optical follow-up campaign. The optical follow-up conce
ntrates on the brightest 94 of the 374 extended sources and is now 97% comp
lete. We have identified 37 clusters of galaxies, for which we present reds
hifts and luminosities. The clusters span a redshift range of 0.0696 < z <
0.83 and a luminosity range of 0.065 < L-X < 8.3 x 10(44) ergs s(-1) [0.5-2
.0 keV] (assuming H-0 = 50 km s(-1) Mpc(-1) and q(0) = 0.5). Twelve of the
clusters have redshifts greater than z = 0.3, eight of which are at luminos
ities brighter than L-X = 3 x 10(44) ergs s(-1) Seventeen of the 37 optical
ly confirmed Bright SHARC clusters have not been listed in any previously p
ublished catalog. We also report the discovery of three candidate "fossil g
roups" of the kind proposed by Ponman et al.