  In the $R$Al(Si,Ge) ($R$: lanthanides) family, both spatial inversion and
time-reversal symmetries are broken. This may offer opportunities to study
Weyl-fermion physics in nontrivial spin structures emerging from a
noncentrosymmetric crystal structure. In this study, we investigated the
anomalous Hall effect (AHE) in NdAlGe via magnetotransport, magnetization, and
magnetic torque measurements down to 40 mK (0.4 K for magnetization). The
single crystals grown by a laser-heated floating-zone method exhibit a single
magnetic phase transition at $T_{\rm M}$ = 13.5 K, where the $T_{\rm M}$ is the
transition temperature. With the magnetic field parallel to the easy
$\lbrack$001$\rbrack$ axis, the AHE gradually evolves as the temperature
decreases below $T_{\rm M}$. The anomalous Hall conductivity (AHC) reaches
$\sim$320 $\Omega^{-1}$cm$^{-1}$ at 40 mK in the magnetically saturated state.
Except in low-temperature low-field plateau phases, the AHC and magnetization
are proportional, and their ratio agrees with the ratios for conventional
ferromagnets, suggesting that the intrinsic AHE occurs by the Karplus-Luttinger
mechanism. Below $\sim$0.6 K, the curves of Hall resistivity against the field
exhibit plateaus at low fields below $\sim$0.5 T, correlating with the plateaus
in the magnetization curve. For the first plateau, the magnetization is one
order of magnitude smaller than the magnetically saturated state, whereas the
AHE is more than half that in the saturated state. This finding under well
below $T_{\rm M}$ suggests that the AHE at the first plateau is not governed by
the magnetization and may be interpreted based on a multipole or spin
chirality.
