One of the main goals of QSO research is to use these objects as a probe of the history of the Universe. Two specific aims are first, to determine the characteristics of the QSO population as a function of redshift, and second, to find the lookback time at which QSOs first appeared, as this provides some measure of the time scale for galaxy formation in the early Universe. Both of these important aims require large and preferably unbiased samples of QSOs. In this chapter, we consider how large samples of QSOs might be obtained through various survey techniques, and how the samples we obtain might be affected by various biases.

The measurable quantity that will result from surveys is the QSO ‘surface density’ dN(F,z)/dΩ i.e., number of QSOs per unit solid angle (square degree) as a function of flux F and redshift z. From this, we can compute the ‘luminosity function’, which is the relative number of AGNs at a given luminosity, and the ‘space density’, which is the total number of sources per unit comoving volume! over some specified luminosity range – when the luminosity function is correctly normalized, the total space density is simply the integral of the luminosity function over its entire range.

The primary goal of QSO surveys then is to determine dN(F,z)/dΩ in an accurate and unbiased fashion. This is a difficult and complicated undertaking because QSOs are faint and their surface density is low; the total surface density of QSOs brighter than B = 21 mag is only ∼40deg-2.