Selected topics on quantum gravity are treated emphasizing more geometrical me- methods and conceptual issues than functional analysis, perturbative expansions and computation of numbers, The lirst part deals with Asymptotic Quantization sheding light on the origin of the Bondi-Meizner-Sachs group in the gravitational radiation theory. The second part is devoted to canonical quantization, which provides the de- detailed quantum dynamics and complements the purely kinematic;)] asympotic descrip- description preset"!Led in the lirsf part.

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