  Combining a new, increased dataset of 8 QSOs covering the Ly-alpha forest at
redshifts 1.5 < z < 3.6 from VLT/UVES observations with previously published
results, we have investigated the properties of the Ly-alpha forest at 1.5 < z
< 4. We have fitted Voigt profiles to the Ly-alpha absorption lines as in
previous studies, and have, for two QSOs, fitted Ly-alpha at z ~ 2.2 and higher
order of Lyman lines down to 3050 Angstrom simultaneously. For a given HI
column density range, the Ly-alpha forest at 1.5 < z < 4 shows the monotonic
evolution, in terms of the line number density and the HI opacity. For higher
column density clouds at 10^{14} cm^(-2),there is a variation in the line
number density from sightline to sightline at z < 2.5. This variation is
stronger for higher column density systems, probably due to more
gravitationally evolved structures at lower z. The correlation strength of the
step optical depth correlation function shows the strong evolution from z ~ 3.3
to z ~ 2.1, although there is a large scatter along different sightlines. The
analyses of the Ly-beta forest at z ~ 2.2 are, in general, in good agreement
with those of the Ly-alpha forest.
