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Cavity spintronics explores light matter interactions at the interface between spintronic and quantum phenomena. Until now, studies have focused on the hybridization between ferromagnets and cavity photons.In this article, we realize antiferromagnetic cavity-magnon polaritons. The collective spin motion in single hematite crystals (α-Fe2O3) hybridizes with 18 - 45 GHz microwave cavity photons with required specific symmetries. We show theoretically and experimentally that the photon-magnon coupling in the collinear phase is mediated by the dynamical Neel vector and the weak magnetic moment in the canted phase by measuring across the Morin transition. The coupling strength g is shown to scale with the anisotropy field in the collinear phase and with the Dzyaloshinskii-Moriya field in the canted phase. We achieve a strong coupling regime both in canted (C > 25 at 300 K) and noncolinear phases (C > 4 at 150 K) and thus coherent information exchange with antiferromagnets These results evidence a generic strategy to achieve cavity-magnon polaritons in antiferromagnets for different symmetries, opening the field of cavity spintronics to antiferromagnetic materials.