  [Abridged] We present FLO (From Lines to Over-densities), a new technique to
reconstruct the hydrogen density field for the Lya forest lines observed in
high resolution QSO spectra. The method is based on the hypothesis that the Lya
lines arise in the low to intermediate density intergalactic gas and that the
Jeans length is the typical size of the Lya absorbers. The reliability of FLO
is tested against mock spectra obtained from cosmological simulations. The
recovering algorithm gives satisfactory results in the range from the mean
density to over-densities of ~30 and reproduces correctly the correlation
function of the density field and the 1D power spectrum on scales between ~20
and 60 comoving Mpc. A sample of Lya forests from 22 high resolution QSO
spectra is analysed, covering the redshift range 1.7<z<3.5. For each line of
sight, we fit Voigt profiles to the lines of the Lya forest, providing the
largest, homogeneous sample of fitted Lya lines ever studied. The line number
density evolution with redshift follows a power-law relation: dn/dz=(166 +/- 4)
[(1+z)/3.5]^{(2.8 +/- 0.2)} (1 sigma errors). The two-point correlation
function of lines shows a signal up to separations of ~2 comoving Mpc; weak
lines (log N(HI)<13.8) also show a significant clustering but on smaller scales
(r<1.5 comoving Mpc). We estimate with FLO the hydrogen density field toward
the 22 observed lines of sight. The redshift distribution of the average
densities computed for each QSO is consistent with the cosmic mean hydrogen
density in the analysed redshift range. The two-point correlation function and
the 1D power spectrum of the delta field are estimated. The correlation
function shows clustering signal up to ~4 comoving Mpc.
