  The quasi-one-dimensional van der Waals compound Bi$_4$Br$_4$ was recently
found to be a promising high-order topological insulator with exotic electronic
states. In this paper, we study the electrical transport properties of
Bi$_4$Br$_4$ bulk crystals. Two electron-type samples with different electron
concentrations are investigated. Both samples have saturation resistivity
behavior in low temperature. In the low-concentration sample, two-dimensional
quantum oscillations are clearly observed in the magnetoresistance
measurements, which are attributed to the band-bending-induced surface state on
the (001) facet. In the high-concentration sample, the angular
magnetoresistance exhibits two pairs of symmetrical sharp valleys with an
angular difference close to the angle between the crystal planes (001) and
(100). The additional valley can be explained by the contribution of the
boundary states on the (100) facet. Besides, Hall measurements at low
temperatures reveal an anomalous decrease of electron concentration with
increasing temperature, which can be explained by the temperature-induced
Lifshitz transition. These results shed light on the abundant surface and
boundary state transport signals and the temperature-induced Lifshitz
transition in Bi$_4$Br$_4$.
