  In inflationary cosmology, the particles constituting the Universe are
created after inflation in the process of reheating due to their interaction
with the oscillating inflaton field. In the bosonic sector, the leading channel
of particle production is the non-perturbative regime of parametric resonance,
preheating, during which bosons are created exponentially fast. Pauli blocking
prohibits the unbounded creation of fermions. For this reason, it has been
silently assumed that the creation of fermions can be treated with perturbation
theory for the decay of individual inflatons. We consider the production of
fermions interacting with the coherently oscillating inflatons. We find that
the actual particle production occurs in a regime of the parametric excitation
of fermions, leading to preheating of fermions. Fermion preheating differs
significantly from the perturbative expectation. It turns out that the number
density of fermions varies periodically with time. The total number of fermions
quickly saturates to an average value within a broad range of momenta $\propto
q^{1/4}$, where $q$ is the usual resonance parameter. The resonant excitation
of fermions may affect the transfer inflaton energy, estimations of the
reheating temperature, and the abundance of superheavy fermions and gravitinos.
Back in the bosonic sector, outside of the parametric resonance bands there is
an additional effect of parametric excitation of bosons with bounded occupation
number in the momentum range $\propto q^{1/4}$.
