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Recently it has been pointed out that the characteristic quantum-gravity scale could be as low as the weak scale in theories with gravity propagating in higher dimensions. The observed smallness of Newton's constant is a consequence of the large compactified volume of the extra dimensions. We investigate the consequences of this supposition for high-energy collider experiments. We do this by first compactifying the higher-dimensional theory and constructing a 3 + 1-dimensional low-energy effective field theory of the graviton Kaluza-Klein excitations and their interactions with ordinary matter. We then consider graviton production processes, and select gamma + E and jet + E signatures for careful study. We find that both a 1 TeV e(+)e(-) collider and the CERN LHC will be able to reliably and perturbatively probe the fundamental gravity scale up to several TeV, with the precise value depending on the number of extra dimensions. Similarly, searches at LEP2 and the Tevatron are able to probe this scale up to approximately 1 TeV. We also discuss virtual graviton exchange, which induces local dimension-eight operators associated with the square of the energy-momentum tensor. We estimate the size of such operators and study their effects on f (f) over bar --> gamma gamma observables. (C) 1999 Elsevier Science B.V.