  A search for heavy resonances decaying into a pair of $Z$ bosons leading to
$\ell^+\ell^-\ell^+\ell^-$ and $\ell^+\ell^-\nu\bar\nu$ final states, where
$\ell$ stands for either an electron or a muon, is presented. The search uses
proton proton collision data at a centre-of-mass energy of 13 TeV corresponding
to an integrated luminosity of 36.1 fb$^{-1}$ collected with the ATLAS detector
during 2015 and 2016 at the Large Hadron Collider. Different mass ranges for
the hypothetical resonances are considered, depending on the final state and
model. The different ranges span between 200 GeV and 2000 GeV. The results are
interpreted as upper limits on the production cross section of a spin 0 or spin
2 resonance. The upper limits for the spin 0 resonance are translated to
exclusion contours in the context of Type I and Type II two-Higgs-doublet
models, while those for the spin 2 resonance are used to constrain the Randall
Sundrum model with an extra dimension giving rise to spin 2 graviton
excitations.
