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The Revival of Kaon Flavour Physics

After years of silence we should witness in the rest of this decade and in the next decade the revival of kaon flavour physics. This is not only because of the crucial measurements of the branching ratios for the rare decays $K^+\toπ^+ν\barν$ and $K_{L}\to π^0ν\barν$ by NA62 and KOTO that being theoretically clean and very sensitive to new physics (NP) could hint for new phenomena even beyond the reach of the LHC without any significant theoretical uncertainties. Indeed simultaneously the advances in the calculations of perturbative and in particular non-perturbative QCD effects in $\varepsilon'/\varepsilon$, $\varepsilon_K$, $ΔM_K$, $K_L\toμ^+μ^-$ and $K_L\toπ^0\ell^+\ell^-$ will increase the role of these observables in searching for NP. In fact the hints for NP contributing to $\varepsilon'/\varepsilon$ have been already signalled last year through improved estimates of hadronic matrix elements of QCD and electroweak penguin operators $Q_6$ and $Q_8$ by lattice QCD and large $N$ dual QCD approach. This talk summarizes in addition to this new flavour anomaly the present highlights of this field including some results from concrete NP scenarios.