  This article presents measurements of the $t$-channel single top-quark ($t$)
and top-antiquark ($\bar{t}$) total production cross sections $\sigma(tq)$ and
$\sigma(\bar{t}q)$, their ratio $R_t=\sigma(tq)/\sigma(\bar{t}q)$. Differential
cross sections for the $\sigma(tq)$ and $\sigma(\bar{t}q)$ processes are
measured as a function of the transverse momentum and the absolute value of the
rapidity of ($t$) and ($\bar{t}$), respectively. The analysed data set was
recorded with the ATLAS detector and corresponds to an integrated luminosity of
4.59 fb$^{-1}$. The cross sections are measured by performing a binned
maximum-likelihood fit to the output distributions of neural networks. The
resulting measurements are $\sigma(tq)=46 \pm 6$ pb, $\sigma(\bar{t}q)=23 \pm
4$ pb, $R_t=2.04 \pm 0.18$, consistent with the Standard Model expectation.
