  After a brief introduction to classical and quantum gravity we discuss
applications of loop quantum gravity in the cosmological realm. This includes
the basic formalism and recent results of loop quantum cosmology, and a
computation of modified dispersion relations for quantum gravity phenomenology.
The presentation is held at a level which does not require much background
knowledge in general relativity or mathematical techniques such as functional
analysis, so as to make the article accessible to graduate students and
researchers from other fields.
