The ATLAS experiment has measured the total proton-proton cross section during the LHC Run-1 at $\sqrt s=7$ and $8~$TeV and in Run-2 at $\sqrt s=13~$TeV using a luminosity dependent approach.
This measurement requires special data-taking conditions with high-$\beta^{*}$ which represent a challenge for the luminosity determination.
The systematic uncertainty associated to the luminosity value represents one of the dominant components of the overall uncertainty on $\sigma_{pp}^{tot}$ and the $\rho$-parameter.
Thanks to the excellent performance and sensitivity of the main ATLAS luminometer, LUCID-2, and of the ancillary measurement based on track-counting algorithms used to estimate the systematic uncertainty, a precision on the luminosity determination of 1.0% (2.15%) was obtained in 2018 (2016) data taking at $\beta^{*}=90~$m ($2.5~$km).

In this work, a description of the luminosity measurement in the Run-2 data taking at $\sqrt s=13~$TeV aimed to measure $\sigma_{pp}^{tot}$ and $\rho$ is given, with emphasis on the ATLAS approach, based on the redundancy of the luminosity information provided by different detectors and methods with different sensitivity to the LHC optic conditions, backgrounds and systematic effects.