  The question that guides our discussion is "how did the geometry and
particles come into being?" To explore this query we suggest the theory of
goyaks, which reveals the primordial deeper structures underlying fundamantal
concepts of contemporary physics. It address itself to the question of the
prime-cause of origin of geometry and basic concepts of particle physics such
as the fundamental fields of quarks and leptons with the spins and various
quantum numbers, internal symmetries and so on; also basic principles of
Relativity, Quantum, Gauge and Color Confinement, which are, as it was proven,
all derivative and come into being simultaneously. The substance out of which
the geometry and particles are made is a set of new physical structures-the
goyaks involved into reciprocal linkage establishing processes. We elaborated a
new mathematical framework, which is a still wider generalization of the
familiar methods of secondary quantization with appropriate expansion over the
geometric objects. One interesting offshoot of it directly leads to the
formalism of operator manifold, which framed our discussion throughout this
paper. It yields the quantization of geometry, which differs in principle from
all earlier studies. Many of the important anticipated properties, basic
concepts and principles of particle physics are appeared quite naturally in the
framework of suggested theory. It predicts a class of possible models of
internal symmetries, which utilize the whole idea of gauge symmetry and
reproduce the known phenomenology of electromagnetic, weak and strong
interactions. Here we focused our attention mainly on developing the
mathematical foundations for our novel viewpoint. We believe that the more
realistic final theory of particles and interactions can be found within the
