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After reviewing the basic aspects of the exactly solvable quantum-correcteddilaton-gravity theories in two dimensions, we discuss a (subjective) selectionof other aspects: a) supersymmetric extensions, b) canonical formalism,ADM-mass, and the functional integral measure, and c) a positive energy theoremand its application to the ADM- and Bondi-masses.Comment: 30 pages. Based on Talks given at Strings 93, Berkeley, May 1993, and  at the Santa Barbara conference "Quantum Aspects of Black Holes". PUPT-141

ASPECTS OF EXACTLY SOLVABLE QUANTUM-CORRECTED 2D DILATON GRAVITY THEORIES