Measurements of the CKM angle $\gamma$ at the LHCb experiment

Two measurements of the Cabibbo-Kobayashi-Maskawa angle $\gamma$ using $B \to D K$ and $B^{0} \to D K^{\ast 0}$ decays are presented in this thesis. The subsequent $D$ meson decays to the $K_{S}^{0} \pi^{+} \pi^{-}$ and $K_{S}^{0} K^{+} K^{-}$ final states are studied using a binned Dalitz plot analysis. The $D$ strong-phase variation over the Dalitz plot is taken from measurements performed at the CLEO-c experiment, making the analysis independent of a model to describe the $D$ decay amplitude. Both measurements are performed using proton-proton collision data collected by the Large Hadron Collider beauty (LHCb) experiment in 2011 and 2012, corresponding to an integrated luminosity of 3 fb$^{-1}$ at centre-of-mass energies $\sqrt{s}=$ 7 TeV and 8 TeV. The value $\gamma=(62\,^{+15}_{-14})^{\circ}$ is measured using $B \to D K$ decays and $\gamma=(71\pm20)^{\circ}$ is measured using $B^{0} \to D K^{\ast 0}$ decays, with a second solution for each value corresponding to $\gamma+180^{\circ}$. The measurements are consistent with the world average value of $\gamma$.