Mixing and $C\!P$ violation in charm decays at LHCb

The LHCb experiment has collected the world's largest sample of charmed hadrons. This sample is used to measure observables related to $D^0 -\overline{D}^0$ mixing, direct $C\!P$ violation and $C\!P$ violation in mixing and interference in the charm sector. In this document, the most recent results from LHCb on the search of direct $C\!P$ violation in $D^0$ and $D_{(s)}^+$ decays are summarised, as well as the first observation of mass difference between neutral charm-meson eigenstates and the most precise measurement of time-dependent $C\!P$ asymmetry in $D^0 \to K^+ K^-$ and $D^0 \to \pi^+ \pi^-$ decays.