  A search for four-top-quark production, $t\bar{t}t\bar{t}$, is presented. It
is based on proton-proton collision data with a center-of-mass energy
$\sqrt{s}$ = 13 TeV collected by the ATLAS detector at the Large Hadron
Collider during the year 2015 and 2016, corresponding to an integrated
luminosity of $36.1$ fb$^{-1}$. Data are analyzed in both the single-lepton and
opposite-sign dilepton channels, characterized by the presence of one or two
isolated electrons or muons with high-transverse momentum and multiple jets. A
data-driven method is used to estimate the dominant background from top-quark
pair production in association with jets. No significant excess above the
Standard Model expectation is observed. The result is combined with the
previous same-sign dilepton and multilepton searches carried out by ATLAS and
an observed (expected) upper limit of 5.3 (2.1) times the four-top-quark
Standard Model cross section is obtained at 95% confidence level. Additionally,
upper limit on anomalous four-top-quark production cross section is set in the
context of an effective field theory model.
