The covariant path integral quantization of the theory of the scalar and spinor fields interacting through the Abelian and non-Abelian Chern - Simons gauge fields in 2 + 1 dimensions is carried out using the De Witt - Fadeev - Popov method. The mathematical ill-definiteness of the path integral of theories with pure Chern - Simons' fields is remedied by the introduction of the Maxwell or Maxwell-type (in the non-Abelian case) terms, which make the resulting theories super-renormalizable and guarantees their gauge-invariant regularization and renormalization. The generating functionals are constructed and shown to be the same as those of quantum electrodynamics (quantum chromodynamics) in 2 + 1 dimensions with the substitution of the Chern - Simons propagator for the photon (gluon) propagator. By constructing the propagator in the general case, the existence of two limits; pure Chern - Simons and quantum electrodynamics (quantum chromodynamics) after renormalization is demonstrated.

The Batalin - Fradkin - Vilkovisky method is invoked to quantize the theory of spinor non-Abelian fields interacting via the pure Chern - Simons gauge field and the equivalence of the resulting generating functional to the one given by the De Witt - Fadeev - Popov method is demonstrated.

The S-matrix operator is constructed, and starting from this S-matrix operator novel topological unitarity identities are derived that demand the vanishing of the gauge-invariant sum of the imaginary parts of the Feynman diagrams with a given number of intermediate on-shell topological photon lines in each order of perturbation theory. These identities are illustrated by explicit examples.