  We study the classical and quantum models of a Friedmann-Robertson-Walker
(FRW) cosmology in the framework of the gravity theory proposed by Ho\v{r}ava,
the so-called Ho\v{r}ava-Lifshitz theory of gravity. Beginning with the ADM
representation of the action corresponding to this model, we construct the
Lagrangian in terms of the minisuperspace variables and show that in comparison
with the usual Einstein-Hilbert gravity, there are some correction terms coming
from the Ho\v{r}ava theory. Either in the matter free or in the case when the
considered universe is filled with a perfect fluid, the exact solutions to the
classical field equations are obtained for the flat, closed and open FRW model
and some discussions about their possible singularities are presented. We then
deal with the quantization of the model in the context of the Wheeler-DeWitt
approach of quantum cosmology to find the cosmological wave function. We use
the resulting wave functions to investigate the possibility of the avoidance of
classical singularities due to quantum effects.
