2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71713We 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.It is a short submission variant of math.DG/0205190 reduced to 48 pages with modifications requested by the Editor of IJMMSDifferential GeometryGeneral Relativity and Quantum CosmologyHigh Energy Physics - TheoryMathematical Physics15A66, 58B20, 53C60, 83C60, 83E15text