We present a model for the Lyman-alpha absorbers that treats all objects (f
rom the low-density forest clouds to the dense damped systems) in a unified
description. This approach is consistent with an earlier model of galaxies
(luminosity function, metallicity) but also with the known description of
the density field in the small-scale non-linear regime. We consider two cos
mological models: a critical universe Omega = 1 with a CDM power-spectrum,
and an open CDM universe with Omega(0) = 0.3, Lambda = 0. we reproduce the
available data on column density distribution as a function of redshift, th
e value of the main new parameter, the background ionizing UV flux, being c
onsistent with the observed limits. This allows a quantitatively trustable
analytical description of the opacity, mass, size, velocity dispersion and
metallicity of these absorbers, over a range of column densities spanning 1
0 orders of magnitude. Moreover, together with an earlier model of galaxy f
ormation this draws a unified picture of the redshift evolution of structur
es in the universe, from underdense clouds to massive high density galaxies
, from weak to very deep potential wells.