The Large Hadron Collider (LHC) is the most powerful and complex particle accelerator ever built. The ATLAS and the CMS are the two multipurpose particle detectors at the LHC, designed to cover a wide range of physics measurements. Three physics studies performed using data of proton-proton collisions collected with the ATLAS detector are presented. The identification of jets originating from b quarks, also known as b-tagging, is a crucial tool for many physics analyses at the LHC. This thesis presents a calibration of the b-tagging efficiency for high transverse momentum jets using a new calibration technique. This analysis is based on template fits and uses multi-jet events, which allows to perform the calibration for jets with transverse momenta up to 1200 GeV. This thesis also describes a completed and connected technical project on the development of the b-tagging ATLAS software. Dark Matter (DM) is a new phenomenon introduced to explain astrophysical observations. The nature of DM is one of the most important subjects of investigations in the modern physics, and many of these investigations are carried out at the LHC. A search for DM production in association with a pair of heavy flavour quarks has been recently performed in ATLAS at a centre-of-mass energy √s = 8 TeV under the Effective Field Theory approach. A re-interpretation of the results of this search under assumption of the simplified models is presented. A set of simplified models is considered with various DM masses, masses of the spin-0 exchange particle, that mediates the interaction between DM and the regular matter, and various values of couplings. Benchmark models are chosen to be used in the DM searches at √s = 13 TeV. The last part of the thesis presents a search for DM production in association with a pair of top quarks performed under assumption of the simplified models with spin-0 mediator, using the data collected at a centre-of-mass energy √s = 13 TeV. The observed data are shown to be in good agreement with the Standard Model predictions, and upper limits are set on a ratio between the observed DM production cross section and the value expected by the simplified model.