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The study of computus, i.e. the medieval science of the reckoning of time, has lately received considerable attention. The focus of this research, however, has been on the few texts that can be readily attributed to well-known authors, leaving the impression that this science was understood and advanced only by a single scholar every 100 years, who appear to have been self-educated geniuses rather than the product of an intellectual milieu, a scientific tradition. In this respect, the present study of the famous Munich Computus closes the gap between the scientific writings of Isidore of Seville and those of the Venerable Bede. The Munich Computus, though known and studied for the past 130 years, has never been edited. This desideratum is met by the present study, applying editorial techniques that aim at placing every single passage of this text in its scientific context by tracing the development of the underlying ideas in the 200 years prior to the composition of the Munich text in AD 719, as well as analyzing its impact on the Carolingian renaissance; the Latin text is accompanied by an English translation and comprehensive commentary of its technical content. The introduction to the edition proper places the Munich Computus within the history of computistics, discusses the history of this text from its compilation in southern Ireland in AD 719 to the transfer of the only known manuscript containing this text from St Emmeram in Regensburg to the Bayerische Staatsbibliothek in Munich. In particular, the detailed source analysis brings to light important computistical texts previously hidden in the manuscripts, most importantly the Computus Einsidlensis, which makes it possible to define, for the first time, the immense Irish contribution to the history of science in the century between Isidore and Bede and with this to put the latter's scientific achievements into perspective.