Measurements of CP violation in B^-→ DK^*- decays, including the sensitivity to the CKM angle gamma, are presented in this thesis. Decays of the D⁰ meson to K^-π⁺, K^-K⁺, π^-π⁺, π^-K⁺, K^-π⁺π^-π⁺, π^-π⁺π^-π⁺, and π^-K⁺π^-π⁺ are investigated. Observables are measured that are sensitive to the CKM angle gamma and the hadronic parameters of the decay r_B and delta_B. These measurements are performed using proton-proton collision data collected by the Large Hadron Collider beauty (LHCb) experiment from 2011 to 2016. These data correspond to the largest yields observed in these modes. The world's first CP violation measurements in four-body D⁰ decay modes using the B^- → DK^*- channel are presented. The first evidence of the B^- → DK^*- mode, where the D⁰ decays to π^-K⁺, is also obtained with a signal significance of 4.2sigma. A value of gamma = 40.9° is measured with a 1 sigma confidence interval of [25, 58]°, and 2sigma confidence intervals of [10, 87]° and [97,167]°, which is consistent with the world average measurement of gamma. The world's most precise value of r_B = 0.113^+0.017_-0.019 for B^- → DK^*- decays is measured.