Volume IV.A contains the first part of Refectio. It publishes the first ever attempt at a full scale reconstruction of Heraclitus' book out of the ca. 200 fragments and ca. 50 unparalleled opinions attributed to him in all the Ancient and Medieval sources that have come down to us on his treatise and doctrine.All the items are presented in a the order dictated or suggested by their language and content so as to (re)create the natural flow of the philosopher's discourse.The reconstructed treaty falls naturally into three parts: a Proem attacking the 'many' and a number of prominent sages with digressions on various subjects, a 'Meta-physical' part consisting of an epistemo-/psycho-/logico-ethical introduction, a Doctrine of the One and the oneness of opposites with a series of examples and a number of digressions, and a Physical part dwelling on cosmogony, cosmology, psychology and astrometeorology.The reconstruction proper is followed by a detailed commentary on the methodology applied, a no less detailed argumentation of every step of the restoration process and a thorough discussion of the possible variants, lacunae and still unsolved problems.This book complements vols. II.A.1-4 (Traditio), III.1 (Memoria), III.2 (Placita) and III.3.B/i-iii (Fragmenta) published earlier (1999-2008) and winds up the edition of all the most relevant Ancient texts related to Heraclitus and his lost treatise.