  The quest to understand better the nature of the initial cosmological
singularity is with us since the discovery of the expanding universe. Here, we
propose several non-flat models, among them the standard cosmological scenario
with a critical cosmological constant, the Einstein-Cartan cosmology, the
Milne-McCrea universe with quantum corrections and a non-flat universe with
bulk viscosity. Within these models, we probe into the initial singularity by
using different techniques. Several nonsingular universes emerge, one of the
possibilities being a static non-expanding and stable Einstein universe.
