Abstract
We propose a microscopic translationally invariant glass model which exhibits two-level tunneling systems, and shows the salient low-temperature anomalies of glassy systems. Results so far obtained are in good accord with experiment. Qualitative universality is due to the collective origin of the glassy potential energy landscape. However, we obtain a simple explanation also for the mysterious so-called quantitative universality that manifests itself, e.g., in the unusually weak dependence of values for the internal friction plateau on substance or system parameters.