General equations of the unified field theory, based on the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of metric-affine space, and describe the distribution and motion of matter, which represents the curvature and torsion of the space-time. Equations, describing spherically symmetric fields, are derived for various cases: a gravitational field in vacuum and arbitrary material field. Equations, describing the uniform isotropic field, are derived for closed and open uniform isotropic models of the universe for the gravitational field in vacuum and for an arbitrary material field. The respective solutions without singularities were obtained for these cases. It is shown that there is no necessity to quantize the obtained general equations.