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

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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 (MB < -23) in a 153 deg² area, covered by the six ``deep'' fields, intended to obtain significant statistics down B ≃ 18.75 with unprecedented photometric accuracy. From this database, QSO counts are determined in the magnitude range 17 < B < 18.75.