## Loop Quantization of Geometry

Loop quantum gravity aims at a mathematically rigorous quantization of general relativity. It relies on a reformulation of gravity as a gauge field theory with constraints, which is canonically quantized. The classical configuration space A is formed by connections in some principal fibre bundle and gets compactified during quantization. The resulting space can be seen as the spectrum of an appropriate C*-algebra of bounded functions on A or as a projective limit of powers of the structure group. Moreover, it exhibits a canonical measure induced by the Haar measure. In my talk, I am going to present the background and the basic structures of the theory. If time permits, I will also discuss applications to the quantization of geometric entities like area or how diffeomorphism invariance restricts the freedom in quantizing the full theory.

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