  The first part of this work deals with the development of a natural
differential calculus on non-commutative manifolds. The second part extends the
covariance and equivalence principle as well studies its kinematical
consequences such as the arising of gauge theory. Furthermore, a manifestly
causal and covariant formulation of quantum field theory is presented which
surpasses the usual Hamiltonian and path integral construction. A particular
representation of this theory on the kinematical structure developed in section
three is moreover given.
