The Hamburg/ESO survey for bright QSOs III. A large flux-limited sample ofQSOs

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 a re in the interval 13 less than or similar to B-J less than or similar to 1 7.5, redshifts range within 0 < z < 3.2. More than 50% of the objects in th e sample are new discoveries. We describe the selection techniques and disc uss sample completeness and potential selection effects. There is no eviden ce for redshift-dependent variations of completeness: in particular, low-re dshift 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 QSOs multiply imaged due to gravitational lensing. The sample forms the largest homogeneous set of bright QSOs currently in existence, useful for a variety of statistical stu dies. We have redetermined the bright part of the optical quasar number-mag nitude relation. We confirm that the Palomar-Green survey is significantly incomplete, but that its degree of incompleteness has recently been overest imated.