This thesis describes the search for resonant and non-resonant Higgs boson pair production in the b ¯bτ +τ − decay channel. The main focus of this document is on the final state where both τ -leptons decay hadronically. The search is performed using 36.1 fb−1 of data collected by the ATLAS detector in proton-proton collisions at a centre-of-mass energy of 13 TeV during 2015 and 2016. The cross-section for non-resonant di-Higgs production is found to be 16.4 times the Standard Model prediction in the fully hadronic channel at a 95% confidence level. Combining the result with the semi-leptonic channel produces a measured signal strength of µ = 12.7 at a 95% confidence level when compared to the Standard Model prediction. Resonant Higgs boson pair production excludes bulk Randall-Sundrum gravitons GKK in the mass range 325 GeV < mGKK < 885 GeV for k/MP L = 1. For the simplified hMSSM minimal supersymmetric model for tan β = 2, resonances are excluded in the mass range 305 GeV < mH < 402 GeV. Finally, a re-interpretation of the Higgs boson pair production analysis is presented as a search for third-generation scalar leptoquarks. Pair-produced third-generation scalar leptoquarks decaying to bτ bτ are excluded at 95% confidence level for mLQ < 1030 GeV.