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We present the theory of Y^n - space, which is essentially different from E. Cartan's theory and that is physically more close to the theory of A. Einstein, but from a mathematical point of view, our theory is distinctive from both A. Einstein and E. Cartan theories. The Geometry of Y^n-space generated by the metric and torsion tensors; we obtained results on the structure of curvature tensor. Geodesics in Y^n space is depended on both metric and torsion tensors, which describe it geometry and don't coincide with geodesics in Riemannian space with the same metric. We considered the hypersurfaces in Y^n and introduced the analog of second fundamental tensor. In Y^n-space can be developed the theory of general relativity and Einstein's theory can be obtained as its particular case. We derived the field equations from the variation principle of least action by varying the metric and torsion independently. They determine the metric and torsion tensors of space-time continuum for a given arrangement of energy and matter. These metric and torsion together describe the structure of Y^n - space including the inertial motion of objects and electromagnetic fields in the space-time continuum.