http://arxiv.org/abs/gr-qc/0505057 Elements of Loop Quantum Cosmology Martin Bojowald 30 pages, 4 figures, Chapter contributed to "100 Years of Relativity - Space-time Structure: Einstein and Beyond", Ed. A. Ashtekar (World Scientific) Report-no: AEI-2005-025 "The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to describe them properly, and one has to refer to quantum gravity. A complete quantization of gravity has not yet been developed, but there are many results about key properties to be expected. When applied to cosmology, a consistent picture of the early universe arises which is free of the classical pathologies and has implications for the generation of structure which are potentially observable in the near future."