  We present a catalogue of absorption lines obtained from the analysis of the
ultra-violet spectra of 66 quasars. The data were acquired with the Faint
Object Spectrograph of the HST as part of the Quasar Absorption Line Survey, a
Key Project for the first four cycles of HST observations. This is the third of
a series of catalogues of absorption lines produced from the survey and
increases the number of quasars whose higher resolution (R=1300) spectra we
have published from 17 to 83. The general properties and execution of the
survey are reviewed, including descriptions of the final sample of observed
objects and the algorithmic processes used to construct the catalogue. The
detection of a single damped Ly-a system in a path length of Delta_z=49 yields
an observed number of damped systems per unit redshift of
(dN/dz)_{damp}(z=0.58)=0.020 with 95% confidence boundaries of 0.001 to 0.096
systems per unit redshift. We include notes on our analysis of each of the
observed quasars and the absorption systems detected in each spectrum. Some
especially interesting systems include low redshift Ly-a absorbers suitable for
extensive follow-up observations (in the spectra of TON28 and PG1216+069),
possibly physically associated pairs of extensive metal line absorption systems
(e.g., in the spectrum of PG0117+213), and systems known to be associated with
galaxies (e.g., in the spectrum of 3C232).
