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In these lectures I review, in as much pedagogical way as possible, varioustheoretical ideas and motivation for violation of CPT invariance in some modelsof Quantum Gravity, and discuss the relevant phenomenology. Since the subjectis vast, I pay particular emphasis on the CPT Violating decoherence scenariofor quantum gravity, due to space-time foam. In my opinion this seems to be themost likely scenario to be realised in Nature, should quantum gravity beresponsible for the violation of this symmetry. In this context, I also discusshow the CPT Violating decoherence scenario can explain experimental``anomalies'' in neutrino data, such as LSND results, in agreement with therest of the presently available data, without enlarging the neutrino sector.Comment: 74 pages LATEX, Submitted to Lect. Notes Phys. (Springer), based on  invited lectures at the 40th Winter School in Poland, February 200

CPT Violation and Decoherence in Quantum Gravity