The top quark is the most massive particle in the SM, with a mass of the order of ∼ 170 GeV. The top quark mass, together with the elements of the CKM mixing matrix, is the only free parameter of the top quark sector of the SM. Therefore, it cannot be calculated from first principles and has to be determined experimentally. In this presentation, we will discuss the significance of the top quark mass in the Standard Model (SM) and its relevance in the search for physics beyond the Standard Model (BSM). We will introduce the different methods and approaches used to measure this parameter, focusing on a method based on the measurement of the differential $t\bar{t}$+jet cross section. This method has led to very precise results in various LHC analyses. Furthermore, we will describe the ongoing development of this method at IFIC using the 13 TeV $pp$ collision data recorded by the ATLAS detector at the LHC. This implementation takes advantage of state-of-the-art methods, such as a Machine Learning (ML) model for the reconstruction of the $t\bar{t}$+jet and $t\bar{t}$ systems, and the Profile Likelihood Unfolding technique (PLU) for correcting the data from detector level to parton level.