This thesis presents a search for resonant and standard model non-resonant di-Higgs production in theb¯bτ +τ− decay channel, with the semi-leptonic ditau state. The search uses data collected by the ATLAS experiment at the LHC of pp-collisions at √s=13 TeV during 2015 and 2016, corresponding to an instantaneous luminosity of 36:1fb-1. No deviation from the Standard Model prediction is observed. For the non-resonant standard model di-Higgs production an upper limit is set on the cross-section compared to the Standard Model prediction,σ/σSM< 24:44 @ 95%CL. Upper limits are set on the cross-section times branching ratio for the resonant searches, where the results are interpreted in terms of constraints on a 2HDM heavy scalar Higgs model and a Randall-Sundrum Kaluza-Klein graviton model. The use of Support Vector Machines is investigated and benchmarked against the nominal results of the Boosted Decision Tree multivariate analysis, in pursuit of potential future improvements.