  A search is conducted for new resonant and non-resonant high-mass phenomena
in dielectron and dimuon final states. The search uses 36.1 fb$^{-1}$ of
proton-proton collision data, collected at $\sqrt{s}$ = 13 TeV by the ATLAS
experiment at the LHC in 2015 and 2016. No significant deviation from the
Standard Model prediction is observed. Upper limits at 95% credibility level
are set on the cross-section times branching ratio for resonances decaying into
dileptons, which are converted to lower limits on the resonance mass, up to 4.1
for the E$_{6}$-motivated Z'$_{\chi}$. Lower limits on the $qq \ell\ell$
contact interaction scale are set between 24 TeV and 40 TeV, depending on the
model.
