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The aim of Geometric Measure Theory (GMT) is to study geometric properties of functions/sets in a measure theoretic sense. Such necessity arises in a natural way when studying minimizers of a large class of variational problems. Due to the impossibility of showing existence of minimizers directly in a class of regular functions (either due to the formation of singularities or to the applicability of the direct method), it is necessary to enlarge the space of competitors and consider functions whose differentials are represented by measures instead of continuous functions, the so-called BV functions. Several notions of differentiability and geometric properties in BV can be defined in a measure-theoretic sense. The striking and powerful achievement of GMT is that indeed such properties, defined in a functional analytic way, turn out to have an actual geometric counterpart, in a more classical sense. In fact, exploiting the minimality assumptions and a set of robust techniques, one can show that for a large class of variational problems the minimizers in the BV space are actually regular functions.