Modern Geometrical Machinery.- Introduction.- Smooth Manifolds.- Fibre Bundles.- Jet Spaces.- Path Integrals: Extending Smooth Geometrical Machinery.- Dynamics of High -Dimensional Nonlinear Systems.- Mechanical Systems. Physical Field Systems.- Nonlinear Control Systems.- Human - Like Biomechanics.- Neurodynamics.- Psycho -Socio - Economic Dynamics.- Appendix: Tensors and Functors.- Elements of Classical Tensor Analysis.- Categories and Functors.- References.- Index.