In 1968, the National Bureau of Standards (NBS) published Special Publication 298 Quantitative Electron Probe Microanalysis, which contained proceedings of a seminar held on the subject at NBS in the summer of 1967. This publication received wide interest that continued through the years far beyond expectations. The present volume, also the result of a gathering of international experts, in 1988, at NBS (now the National Institute of Standards and Technology, NIST), is intended to fulfill the same purpose. After years of substantial agreement on the procedures of analysis and data evaluation, several sharply differentiated approaches have developed. These are described in this publi cation with all the details required for practical application. Neither the editors nor NIST wish to endorse any single approach. Rather, we hope that their exposition will stimulate the dialogue which is a prerequisite for technical progress. Additionally, it is expected that those active in research in electron probe microanalysis will appreciate more clearly the areas in which further investigations are warranted.