Physics with Same-sign Dilepton and Multilepton Event

The Higgs boson was observed in 2012, completing the last missing piece in the Standard Model. While research that culminated with the LHC has established the Standard Model as a successful theory, there are still many unanswered questions. Studying events with same-sign dilepton and multilepton may help to gain insight into those questions. This dissertation reports on two searches for rare Standard Model processes, using proton-proton collisions data at a center-of-mass energy of $\sqrt{s}=13$ TeV recorded by the ATLAS detector at CERN's Large Hadron Collider between years 2015-2018. Both searches are conducted with same-sign dilepton and multilepton final states, where leptons are considered to be either electrons or muons. The first is a search for the associated production of the Higgs boson with a top quark pair ($t\bar{t}H$) in same sign dilepton and multilepton final states. A total of 6 final states, defined by the number and flavor of charged-lepton candidates in each event, and 25 event categories are defined to simultaneously search for the $t\bar{t}H$ signal and constrain several leading backgrounds. An excess of events consistent with $t\bar{t}H$ production, over the expected background from Standard Model processes, is found with an observed significance of 1.8 standard deviations, compared to an expectation of 3.1 standard deviations. Assuming Standard Model branching fractions, the measured $t\bar{t}H$ production cross section is $\sigma_{t\bar{t}H} = 294^{+182}_{-162}$~fb, consistent with the Standard Model prediction. The production rate of the $t\bar{t}W$ process is found to be higher than the theoretical prediction. The impact on the $t\bar{t}H$ cross section measurement of the assumptions made on the $t\bar{t}W$ background modeling is discussed. The second is a search for four-top-quark production with same-sign dilepton and multilepton events. A multivariate discriminant using information based on jet multiplicity, jet flavor and event kinematics are used to separate signal from the background, and dedicated control regions are used to constrain dominant backgrounds. The four-top-quark production cross section is measured to be $24^{+7}_{-6}$~fb, assuming the Standard Model four-top-quark properties. This corresponds to an observed (expected) signal significance of 4.3 (2.4) standard deviations and provides the first evidence for this process.