  This series of lectures gives a simple and self-contained introduction to the
non-perturbative and background independent loop approach of canonical quantum
gravity. The Hilbert space of kinematical quantum states is constructed and a
complete basis of spin network states is introduced. An application of the
formalism is provided by the spectral analysis of the area operator, which is
the quantum analogue of the classical area function. This leads to one of the
key results of loop quantum gravity: the derivation of the discreteness of the
geometry and the computation of the quanta of area. Finally, an outlock on a
possible covariant formulation of the theory is given leading to a "sum over
histories" approach, denoted as spin foam model. Throughout the whole lecture
great significance is attached to conceptual and interpretational issues. In
particular, special emphasis is given to the role played by the diffeomorphism
group and the notion of observability in general relativity.
