The key notions of the differential and Riemannian geometry necessary for understanding the General Relativity are introduced here. We provide the reader with the necessary tools for study the properties of black holesand their interaction with matter and fields. We tried to omit unnecessary details and to make the presentation simpler. We focus on an explanation of the basic concepts and explicit formulas, which can be used for concrete calculations, and give hints, which might be used to simplify these calculations.
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