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We re-examine the Lem\^aitre-Tolman-Bondi (LTB) solutions with a dust sourceadmitting symmetry centers. We consider as free parameters of the solutions theinitial value functions: $Y_i$, $\rho_i$ and $\Ri$, obtained by restricting thecurvature radius, $Y\equiv \sqrt{g_{\theta\theta}}$, the rest mass density,$\rho$, and the 3-dimensional Ricci scalar of the rest frames, $\R$, to anarbitrary 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 anadimensional scale factor $y=Y/Y_i$, we show that the dynamics, regularityconditions and geometric features of the models are determined by $\rho_i$,$\Ri$ and by suitably constructed volume averages and contrast functionsexpressible in terms of invariant scalars defined in $\Ti$. These quantitieslead to a straightforward characterization of initial conditions in terms ofthe nature of the inhomogeneity of $\Ti$, as density and/or curvatureoverdensities (``lumps'') and underdensities (''voids'') around a symmetrycenter. In general, only models with initial density and curvature lumps evolvewithout shell crossing singularities, though special classes of initialconditions, associated with a simmultaneous big bang, allow for a regularevolution for initial density and curvature voids. Specific restrictions arefound so that a regular evolution for $t>t_i$ is possible for initial voids. Astep-by-step guideline is provided for using the new variables in theconstruction of LTB models and for plotting all relevant quantities.Comment: 36 pages, 41 graphs grouped into 12 figures. Revtex with BoxedEPSF  macros for embedding figure

A new approach to initial value variables for the Lema$icirc$tre$ndash$Tolman$ndash$Bondi dust solutions