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In Einstein's gravitational theory, the spacetime is pseudoRiemannian, that is, it has vanishing torsion and vanishing nonmetricity. In this work we investigate theories of gravitation in terms of nonRiemannian spacetime geometries, then couple electromagnetic and spinor fields to this nonRiemannian gravity. In addition, we treat the Dirac equation containing torsion and nonmetricity of spacetime by lifting the tangent bundle to the spinor bundle. In order to gain physical insights on torsion and nonmetricity we look at the low energy limit of the Dirac equation via the FoldyWouthuysen transformation. Finally we apply all these mathematical concepts to a physical phenomenon; solar neutrino problem. This problem is solved by the assumption of neutrino oscillations and it is seen that the torsion of spacetime contributes to the oscillations depending on the polarization of spin states of mass eigenstates and this contribution is of the order of the Planck scale. This book is an extended version of my Ph.D. thesis completed under the supervision of Prof.Dr. Tekin DEREL? in the Middle East Technical University, Ankara, Turkey at 2001.
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