  Metallic iridium oxides (iridates) provide a fertile playground to explore
new phenomena resulting from the interplay between topological protection,
spin-orbit and electron-electron interactions. To date, however, few studies of
the low energy electronic excitations exist due to the difficulty in
synthesising crystals with sufficiently large carrier mean-free-paths. Here, we
report the observation of Shubnikov-de Haas quantum oscillations in
high-quality single crystals of monoclinic SrIrO$_3$ in magnetic fields up to
35~T. Analysis of the oscillations reveals a Fermi surface comprising multiple
small pockets with effective masses up to 4.5 times larger than the calculated
band mass. \textit{Ab-initio} calculations reveal robust linear band-crossings
at the Brillouin zone boundary, due to its non-symmorphic symmetry, and overall
we find good agreement between the angular dependence of the oscillations and
the theoretical expectations. Further evidence of strong electron correlations
is realized through the observation of signatures of non-Fermi liquid transport
as well as a large Kadowaki-Woods ratio. These collective findings, coupled
with knowledge of the evolution of the electronic state across the
Ruddlesden-Popper iridate series, establishes monoclinic SrIrO$_3$ as a
topological semimetal on the boundary of the Mott metal-insulator transition.
