  We use magnetization measurements, high-resolution angle-resolved
photoemission spectroscopy (ARPES), and density functional theory (DFT)
calculations to study the electronic properties of Au${}_{2}$Pb, a topological
superconductor candidate. The magnetization measurements reveal three
discontinuities at 40, 51, and 99~K that agree well with reported structural
phase transitions. ARPES measurements of the Au${}_{2}$Pb (111) surface at
110~K shows a shallow hole pocket at the center and flower-petal-like surface
states at the corners of the Brillouin zone. These observations match the
results of DFT calculations relatively well. The flower-petal-like surface
states appear to originate from a Dirac like dispersion close to the zone
corner. For the Au${}_{2}$Pb (001) surface at 150~K, ARPES reveals at least one
electron pocket between the $\Gamma$ and $M$ points, consistent with the DFT
calculations. Our results provide evidence for the possible existence of Dirac
state in this material.
