The paper by Michal Czakon, Paul Fiedler, and Alexander Mitov presents the next-to-next-to-leading order (NNLO) QCD corrections to the total cross-section for top quark pair production ($gg \rightarrow t\bar{t} + X$) at hadron colliders. This completes the set of NNLO QCD corrections to the total top pair production cross-section. The authors use a combination of fixed-order results and soft-gluon resummation to estimate the theoretical uncertainty, which is about 3% at the LHC and 2.2% at the Tevatron. They observe good agreement between the Standard Model predictions and experimental measurements, highlighting the high precision of this observable. The high precision allows for more detailed scrutiny of parton distribution functions and new physics searches. The paper also includes detailed calculations of the NNLO corrections and fits for the top mass dependence of the cross-section, demonstrating the robustness of the theoretical predictions.The paper by Michal Czakon, Paul Fiedler, and Alexander Mitov presents the next-to-next-to-leading order (NNLO) QCD corrections to the total cross-section for top quark pair production ($gg \rightarrow t\bar{t} + X$) at hadron colliders. This completes the set of NNLO QCD corrections to the total top pair production cross-section. The authors use a combination of fixed-order results and soft-gluon resummation to estimate the theoretical uncertainty, which is about 3% at the LHC and 2.2% at the Tevatron. They observe good agreement between the Standard Model predictions and experimental measurements, highlighting the high precision of this observable. The high precision allows for more detailed scrutiny of parton distribution functions and new physics searches. The paper also includes detailed calculations of the NNLO corrections and fits for the top mass dependence of the cross-section, demonstrating the robustness of the theoretical predictions.