Abstract
General Relativity describes gravity in geometrical terms. This sug-gests that quantising such theory is the same as quantising geometry.The subject can therefore be called quantum geometry and one maythink that mathematicians are responsible of this subject. Unfortunatelymost mathematicians are not aware of this beautiful area of study. Herewe give a basic introduction to what quantum geometry means to a com-munity working in a theory known as loop quantum gravity. It is directedtowards graduate or upper students of physics and mathematics. We doit so from a point of view of a mathematician.
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