The statistical properties of the spectrum from large symmetric matrices are investigated. In these matrices the elements are chosen from a power-law distribution p(x) = ا&nu;اx &nu;&minus;1 with &minus;2 &le; &nu; &le; 1. Universality classes or stable laws are explored by studying the density of states &rho;(E) and the distribution of eigenvalue spacings P(s). Various regimes could be identified as a function of the disorder strength parameter &nu;. For 0 < &nu; < 1, the density of states obeys the simple semicircular law, and P(s) follows the Wigner surmise. For &nu; < 0, various zones separated by energy-dependent boundaries are observed. Furthermore, in the limit &nu;&rarr; 0, we find a density of states that corresponds to the sparse matrix limit, with the characteristic singularity &rho;(E) 1/E . However, in this limit the spacing distribution exhibits power laws tails instead of the well known Brody form.