Separation des representations unitaires irreductibles des groupees de lie nilpotents; class operators as intertwining maps into the group algebra; on fine gradings of real forms of sl(n,C); review of Seiberg - written model; quantum integrable systems and zonal spherical functions; torsion, current algebra and Hamiltonian quantization; weak and strong separation properties in hierarchies of nonlinear quantum time evolutions; lie super-algebraisation of BRST-BFV covariant quantization; a geometric construction of solutions of the DKP-heirarchy; explicit calculations of solutions of heat equations on some lie groups; quantum homogeneous vector bundles and representations of quantum groups; frame, cotangent and tangent bundles of the quantum plane. (Part contents).