Quantum Gravity, Cosmology, (Liouville) Strings and Lorentz Invariance

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I review some aspects of non-critical strings in connection with Lorentz-Invariance violating approaches to quantum gravity. I also argue how non-critical strings may provide a unifying framework where string Cosmology and quantum gravity may be tackled together.
25 pages LATEX, uses special macros, invited talk at Beyond the Desert 2002, Oulu (Finland), June 2-7 2002 minor typos corrected, references added

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