The author summarizes the acquisitions on the current status of the manuscript and printed tradition of Fibonacci’s treatise and demonstrates the need of preparing a critical edition of the work. He points out that in the current state of the preparatory work of this edition it’s not possible to provide a genuine stemma codicum yet, but he proposes only some hypotheses about the reciprocal relationships of the manuscript witnesses. The paper ends with an essay of the critical edition in preparation, that is the dedicatory epistle to Michael Scotus and the prologue of the treatise: the critical text is equipped with an apparatus of variants and is provided with a new and original English translation.