  We re-examine the Lem\^aitre-Tolman-Bondi (LTB) solutions with a dust source
admitting symmetry centers. We consider as free parameters of the solutions the
initial value functions: $Y_i$, $\rho_i$ and $\Ri$, obtained by restricting the
curvature radius, $Y\equiv \sqrt{g_{\theta\theta}}$, the rest mass density,
$\rho$, and the 3-dimensional Ricci scalar of the rest frames, $\R$, to an
arbitrary regular Cauchy hypersurface, $\Ti$, marked by constant cosmic time
($t=t_i$). Using $Y_i$ to fix the radial coordinate and the topology
(homeomorphic class) of $\Ti$, and scaling the time evolution in terms of an
adimensional scale factor $y=Y/Y_i$, we show that the dynamics, regularity
conditions and geometric features of the models are determined by $\rho_i$,
$\Ri$ and by suitably constructed volume averages and contrast functions
expressible in terms of invariant scalars defined in $\Ti$. These quantities
lead to a straightforward characterization of initial conditions in terms of
the nature of the inhomogeneity of $\Ti$, as density and/or curvature
overdensities (``lumps'') and underdensities (''voids'') around a symmetry
center. In general, only models with initial density and curvature lumps evolve
without shell crossing singularities, though special classes of initial
conditions, associated with a simmultaneous big bang, allow for a regular
evolution for initial density and curvature voids. Specific restrictions are
found so that a regular evolution for $t>t_i$ is possible for initial voids. A
step-by-step guideline is provided for using the new variables in the
construction of LTB models and for plotting all relevant quantities.
