  In this paper we lay the foundations of causal quantum gravity (CQG), i.e. of
a quantum theory of self-interacting symmetric massless rank-2 tensor gauge
fields, the gravitons, on flat space-time, in the framework of causal
perturbation theory. The causal inductive construction of the S-matrix for
quantum gravity leads to a very satisfactory treatment of the ultraviolet
problem. Here we concentrate on some main fundamental issues that concern the
quantization of the gravitational interactions: the quantization of the free
graviton field, the role of the fermionic ghost vector fields in preserving
perturbative gauge invariance, the construction of the Fock space for the
graviton and the consequent characterization of the subspace for the physical
graviton states. This last point is necessary, together with perturbative gauge
invariance, in order to prove unitary of the S-matrix restricted to the
physical subspace.
