Widely used Inverse Laplace Transformation algorithms applied to magnetic resonance relaxation data do not produce mathematically unique and reversible transforms, but instead produce interpretations of the data. In this sense, the ILT moniker can be somewhat misleading, and in this report the phrase quasicontinuous rendering is preferred. As usually understood, these renderings of amplitude as a function of relaxation rate must be constructed using many more than the 10~15 basis amplitudes that can be determined uniquely from the data alone. Many different amplitude combinations can be found that are mutually compensatory and that can assume wide ranges of values while remaining fully compatible with the data, as discussed in the Introduction and described in more detail in Part 2 of this report.