  Here, we present a detailed study on the temperature and angular dependence
of the Shubnikov-de-Haas (SdH) effect in the semi-metal WTe$_2$. This compound
was recently shown to display a very large non-saturating magnetoresistance
which was attributed to nearly perfectly compensated densities of electrons and
holes. We observe four fundamental SdH frequencies and attribute them to
spin-orbit split, electron- and hole-like, Fermi surface (FS) cross-sectional
areas. Their angular dependence seems consistent with ellipsoidal FSs with
volumes suggesting a modest excess in the density of electrons with respect to
that of the holes. We show that density functional theory (DFT) calculations
fail to correctly describe the FSs of WTe$_2$. When their cross-sectional areas
are adjusted to reflect the experimental data, the resulting volumes of the
electron/hole FSs obtained from the DFT calculations would imply a pronounced
imbalance between the densities of electrons and holes. We find evidence for
field-dependent Fermi surface cross-sectional areas by fitting the oscillatory
component superimposed onto the magnetoresistivity signal to several
Lifshitz-Kosevich components. We also observe a pronounced field-induced
renormalization of the effective masses. Taken together, our observations
suggest that the electronic structure of WTe$_2$ evolves with the magnetic
field. This evolution might be a factor contributing to its pronounced
magnetoresistivity.
