We present a new sample of 415 bright QSOs and Seyfert~1 nuclei drawn from the Hamburg/ESO survey (HES). The sample is spectroscopically 99 % complete and well-defined in terms of flux and redshift limits. Optical magnitudes are in the interval 13 < B_J < 17.5, redshifts range within 0< z < 3.2. More than 50 % of the objects in the sample are new discoveries. We describe the selection techniques and discuss sample completeness and potential selection effects. There is no evidence for redshift-dependent variations of completeness; in particular, low-redshift QSOs - notoriously missed by other optical surveys - are abundant in this sample, since no discrimination against extended sources is imposed. For the same reason, the HES is not biased against multiply imaged QSOs due to gravitational lensing. The sample forms the largest homogeneous set of bright QSOs currently in existence, useful for a variety of statistical studies. We have redetermined the bright part of the optical quasar number-magnitude relation. We confirm that the Palomar-Green survey is significantly incomplete, but that its degree of incompleteness has recently been overestimated.
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