This thesis presents three searches for new resonances in dijet invariant mass spectra. The spectra are produced using √s = 13 TeV proton-proton collision data recorded by the ATLAS detector. New dijet resonances are searched for in the mass range 200 GeV to 6.9 TeV in mass. Heavy new resonances, with masses above 1.1 TeV, are targeted by a high mass dijet search. Light new resonances, with masses down to 200 GeV, are searched for in dijet events with an associated high momentum object (a photon or a jet) arising from initial state radiation. The associated object is used to efficiently trigger the recording of low mass dijet events. All of the analyses presented in this thesis search for an excess of events, localised in mass, above a data-derived estimate of the smoothly falling QCD background. In each search no evidence for new resonances is observed, and the data are used to set 95% C.L. limits on the production cross-section times acceptance times branching ratio for model-independent Gaussian resonance shapes, as well as benchmark signals. One particular benchmark signal which is considered in all of the searches is an axial-vector Z' dark matter mediator model whose parameter space is reduced due to the results presented in this thesis.