This work presents a general, straight-line method to estimate the original oil and gas in-place in a reservoir without restrictions on fluid composition. All past efforts are applicable to only restricted ranges of reservoir fluids. Our work supersedes these and is the first to be applicable to the full range of reservoir fluids—including volatile-oils and gas-condensates. Our work is based on the new generalized material-balance equation recently introduced by Walsh.1 The superiority of the new method is illustrated by showing the error incurred by preexisting calculation methods. Guidelines are offered to help identify when preexisting calculation methods must be abandoned and when the new methods featured herein must be employed. The results of our work are summarized in a set of companion papers. Part 1 discusses applications to initially-undersaturated, volumetric reservoirs and Part 2 discusses applications to initially-saturated and non-volumetric reservoirs.