  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
anholonomic frames with associated nonlinear connection structures. We
emphasize strong arguments for application of Finsler like geometries in modern
string and gravity theory and noncommutative geometry and noncommutative field
theory and gravity.
