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.