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Nonlinear Connections and Clifford Structures

We present an introduction to the geometry of higher order vector and co--vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by higher order nonlinear connections. Geometric applications in locally anisotropic gravity and matter field interactions are considered. This article contains a part of material given by these authors and P. Stavrinos in theirs lectures.