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Universities and other organizations providing higher level education are collectively called Higher Education Institutions. Their detail data, for instance number of students, number of graduates, etc., constitute the basis for several important analyses of the educational systems. This work provides data of the European Tertiary Education Register (ETER), which describes the Educational Institutions of Europe. These data have been gathered through the National Statistical Authorities of all the Countries participant in the ETER Project. However, they include many scattered missing values. Therefore, we have developed and applied an imputation methodology (see "Imputation Techniques for the Reconstruction of Missing Interconnected Data from Higher Educational Institutions, Bruni et al. [3]) to replace the missing values with feasible values being as similar as possible to the original values that have been lost and are now unknown. Thus, we also provide the imputed version of the same dataset, which allows more in-depth analyses of the European Higher Education Institutions. Both datasets (before and after imputation) are provided in two versions: with or without bibliometric information for the Institutions, so the user can also consider these additional information if interested., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships which have, or could be perceived to have, influenced the work reported in this article., (© 2020 The Authors.)