  Detailed measurements of $t$-channel single top-quark production are
presented. They use 20.2 fb$^{-1}$ of data collected by the ATLAS experiment in
proton-proton collisions at a centre-of-mass energy of 8 TeV at the LHC. Total,
fiducial and differential cross-sections are measured for both top-quark and
top-antiquark production. The fiducial cross-section is measured with a
precision of 5.8 % (top quark) and 7.8 % (top antiquark), respectively. The
total cross-sections are measured to be $\sigma_{\mathrm{tot}}(tq) =
56.7^{+4.3}_{-3.8}\;$pb for top-quark production and
$\sigma_{\mathrm{tot}}(\bar{t}q) = 32.9^{+3.0}_{-2.7}\;$pb for top-antiquark
production, in agreement with the Standard Model prediction. In addition, the
ratio of top-quark to top-antiquark production cross-sections is determined to
be $R_t=1.72 \pm 0.09$, with an improved relative precision of 4.9 % since
several systematic uncertainties cancel in the ratio. The differential
cross-sections as a function of the transverse momentum and rapidity of both
the top quark and the top antiquark are measured at both the parton and
particle levels. The transverse momentum and rapidity differential
cross-sections of the accompanying jet from the $t$-channel scattering are
measured at particle level. All measurements are compared to various Monte
Carlo predictions as well as to fixed-order QCD calculations where available.
