This thesis presents measurements of inclusive and differential cross-sections for top quark pair-production in fiducial and full phase-space regions, as well as an analysis of gas compositions in the ATLAS inner detector cooling systems. The inclusive top-anti-top quark production cross-section was measured using a sample of 0.085 1/fb of proton--proton collisions recorded by the ATLAS experiment at centre-of-mass energy of 13 TeV, using dilepton top-anti-top quark events with an opposite-sign ee or ÂµÂµ pair in the final state. The numbers of events with exactly one and exactly two jets originating from b-quarks were counted to determine the top-anti-top quark production cross-section . The efficiency to reconstruct and identify a jet as originating from a b-quark from a top quark decay was extracted simultaneously, minimising the associated systematics. The cross-section was measured to be 749 Â± 57 (stat.) Â± 79 (syst.) Â± 74 (lumi.) pb, giving a total relative uncertainty of 16%. The differential top-anti-top quark production production cross-sections were measured using top-anti-top quark events with one electron and one muon of opposite sign electric charge, and at least two jets, one of which was required to be tagged as containing a b-hadron. Initially, the differential cross-sections were measured in a fiducial phase-space region, using an integrated luminosity of 3.2 1/fb of proton--proton data at a centre-of-mass energy of 13 TeV, recorded by the ATLAS experiment in 2015. Subsequently, the single and double differential cross-sections were measured in both a fiducial phase-space region and the full phase-space, using 36.1 1/fb of proton--proton data at 13 TeV, recorded by the ATLAS experiment in 2015 and 2016. The measured differential cross-sections are compared to predictions of next-to-leading order generators matched to parton showers. Custom ultrasonic instruments have been developed for simultaneous monitoring of binary gas mixture and flow in the ATLAS inner detector. These instruments are sensitive to leaks in the cooling systems of the ATLAS inner detector. Software for on- and off-line analysis of these instruments has been developed and proven with the analysis of the cool-down to operation temperature in January 2016.