  Loop quantum gravity is a physical theory which aims at unifying general
relativity and quantum mechanics. It takes general relativity very seriously
and modifies it via a quantisation. General relativity describes gravity in
terms of geometry. Therefore, quantising such theory must be equivalent to
quantising geometry and that is what loop quantum gravity does. This sounds
like a mathematical task as well. This is why in this paper we will present the
mathematics of loop quantum gravity. We will do it from a mathematician point
of view. This paper is intended to be an introduction to loop quantum gravity
for postgraduate students of physics and mathematics. In this work we will
restrict ourselves to the three dimensional case.
