From the contents 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.