The Standard Model of particle physics is a fundamental theory of the modern physics, describing the elementary particles and their interactions. In the last 50 years it has been subject of several tests in order to validate it and put constraints on its parameters. However, many aspects of the world around us are unclear and they are not explained in the Standard Model. In order to improve our understanding of some of these phenomena, the Large Hadron Collider carries on its work after the Higgs boson discovery, searching for new physics beyond the Standard Model and improving the model itself. A key role in this framework is carried out by the top quark: it has a very large coupling to the Higgs boson and it is also predicted to have large couplings to beyond Standard Model particles. In this contest the production of tttt in proton-proton collisions has a special part, since it is a rare process predicted by the Standard Model and many beyond Standard Model scenarios lead to an enhancement of its cross section. In this thesis a particular channel of decay is considered, the single lepton channel, analysing the data of the proton-proton collisions at a centre of mass energy of 13 TeV collected in the period 2015-2018 by the ATLAS detector at LHC. In order to improve the results already obtained in the past, a multivariate analysis is performed to separate the SM tttt signal from the main tt+jets background. Moreover, a purely Monte Carlo simulation-based method is not expected to model well the tt+jets background in the high jet and b-jet multiplicities regions considered in the thesis, and therefore a data-driven, MC-assisted, approach is adopted to improve the prediction for this background: the ttTRF method. A profile likelihood fit is used for the measurement of the tttt signal strength μ = σ(tttt)/σ(tttt SM). The result is μ = 3.5±0.7(stat.)±1.8(syst.) = 3.5±1.9 which implies an observed (expected) significance of the signal over the background-only hypothesis of 1.8σ (0.5σ). The corresponding measured cross section for the
tttt process is 42±23 fb, compatible with the SM value within 1.3σ. The result is also compatible within 1σ with the recent dilepton same-sign and multilepton channel and the previous single lepton and dilepton opposite-sign channel.
