Next to String theory Loop Quantum Gravity (LQG) is one of the candidates for a theory describing the quantization of gravity. In this talk we want to give a
brief introduction to the concepts and techniques used in LQG.
The starting point of LQG is a Hamiltonian formulation of classical General
Relativity. Using the technique of canonical quantization we present how a
quantum analogue of the classical Einstein -- Equations, the so called Quantum
-- Einstein -- Equations, can be derived. These equations are obviously as
complex as their classical counterpart so we will discuss how they have been
analyzed so far, which approximations have been used and to which extent they
can give us some insight on the properties of space time at the Planck scale.
Finally we will present some aspects of current research in LQG and give an
outlook including a discussion on open problems of LQG.
