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We report a measurement of cross section $\sigma(\nu_{\mu}+{\rmnucleus}\rightarrow\mu^{-}+X)$ and the first measurements of the cross section$\sigma(\bar{\nu}_{\mu}+{\rm nucleus}\rightarrow\mu^{+}+X)$ and their ratio$R(\frac{\sigma(\bar \nu)}{\sigma(\nu)})$ at (anti-)neutrino energies below 1.5GeV. We determine the single momentum bin cross section measurements, averagedover the T2K $\bar{\nu}/\nu$-flux, for the detector target material (mainlyCarbon, Oxygen, Hydrogen and Copper) with phase space restricted laboratoryframe kinematics of $\theta_{\mu}<32^\circ$ and $p_{\mu}>$500 MeV/c. Theresults are $\sigma(\bar{\nu})=\left( 0.900\pm0.029{\rm (stat.)}\pm0.088{\rm(syst.)}\right)\times10^{-39}$ and $\sigma(\nu)=\left( 2.41\\pm0.022{\rm{(stat.)}}\pm0.231{\rm (syst.)}\ \right)\times10^{-39}$ in units ofcm$^{2}$/nucleon and $R\left(\frac{\sigma(\bar{\nu})}{\sigma(\nu)}\right)=0.373\pm0.012{\rm (stat.)}\pm0.015{\rm (syst.)}$.

Measurement of $\bar{\nu}_{\mu}$ and $\nu_{\mu}$ charged current inclusive cross sections and their ratio with the T2K off-axis near detector