The ESO Key-Programme ``A Homogeneous Bright QSO Survey'' - I The Methods and the ``Deep'' Fields

This is the first paper in a series aimed at defining a statistically significant sample of QSOs in the range \( 15 < B < 18.75\) and \( 0.3 < z < 2.2\). The selection is carried out using direct plates obtained at the ESO and UK Schmidt Telescopes, scanned with the COSMOS facility and searched for objects with an ultraviolet excess. Follow-up spectroscopy, carried out at ESO La Silla, is used to classify each candidate. In this initial paper, we describe the scientific objectives of the survey; the selection and observing techniques used. We present the first sample of 285 QSOs (\(M_B < -23\)) in a 153 deg\(^2\) area, covered by the six ``deep'' fields, intended to obtain significant statistics down \(B \simeq 18.75\) with unprecedented photometric accuracy. From this database, QSO counts are determined in the magnitude range \( 17 < B < 18.75\).