  The suggested operator manifold formalism enables to develop an approach to
the unification of the geometry and the field theory. We also elaborate the
formalism of operator multimanifold yielding the multiworld geometry involving
the spacetime continuum and internal worlds, where the subquarks are defined
implying the Confinement and Gauge principles. This formalism in Part II
(hep-th/9812182) is used to develop further the microscopic approach to some
key problems of particle physics.
