  Using high resolution (R ~ 45000), high S/N (20-50) VLT/UVES observations
covering the Lyman-alpha forest at 1.5 < z < 2.4 combined with similar
observations at z > 2.4 from the literature, we have presented the redshift
evolution of the Lyman-alpha forest at 1.5 < z < 4. We applied two parallel
analyses: the tradiational Voigt profile fitting and a statistical measure of
the flux. The general conclusions from both analyses are in good agreement. In
general, the properties of the Lyman-alpha forest at 1.5 < z < 2.4, such as the
different density distribution function, the correlation strengths and the mean
neutral hydrogen opacity, evolve as expected extrapolating from at z > 2.4.
These results suggest the main drive of the redshift evolution of the forest at
1.5 < z < 4 is the Hubble expansion. When combined with the HST observations
from the QSO key project at z < 1.7, a flattening of the line number density
evolution does seem to occur at z ~ 1.2. The result suggests that the ionizing
UV background might not evolve as strongly as a QSO-dominated background,
indicating a contribution to the UV background from galaxies at z < 2. The
lower cut-off Doppler paramter at the fixed column denisty log N = 13.5 shows a
slight increase as z decreases, with a possible local maximum at z ~ 2.9. The
slope of the lower cut-off Doppler parameter is not well-defined with z.
However, it is flatter at z < 3.1 than at z ~ 3.75.
