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This thesis brings together the various techniques of X-ray spectral analysis in order to examine the properties of black holes that vary in mass by several orders of magnitude. In all these systems it is widely accepted that the X-ray emission is produced by Compton up-scattering of lower energy seed photons in a hot corona or accretion flow, and here these processes are examined through a study of the X-ray spectral variability of each source. A new technique is introduced, in which models are fitted to over 2 million X-ray spectra on time-scales as short as 16 ms, and subsequently it is...