Geometry in Quantum Kripke Frames Shengyang Zhong Abstract: Quantum Kripke frames and other related kinds of Kripke frames are introduced. The inner structures of these Kripke frames are studied in detail, and many of them turn out to form nice geometries. To be precise, geometric frames, which are more general than quantum Kripke frames, correspond to projective geometries with a pure polarity; and quantum Kripke frames correspond to irreducible Hilbertian geometries, which play an important role in foundations of quantum theory. Besides, many useful results of these structures are proved.