  In this paper, low regularity local well-posedness results for the
Kadomtsev--Petviashvili--I equation posed in spatial dimension $d =3$ are
proved. Periodic, non-periodic and mixed settings as well as generalized
dispersion relations are considered. In the weak dispersion regime, these
initial value problems show a quasilinear behavior so that bilinear and energy
estimates on frequency dependent time scales are used in the analysis.
