The Ars Notoria is a mediaeval grimoire which was widely distributed and very popular in the 13th-16th century, but virtually unknown until recently. Version B (MS Bibliotheque Nationale Lat. 9336.) is a commentary on the Method which has never been published in English before. The present text is a reorganisation of that commentary into subject order without the loss of any practical detail. All the notae and the full invocations/orations are included, but most of the Latin prayers have been omitted as they do not contribute to the methods effectiveness. The Ars Notoria is still very relevant in the 21st century because it contains detailed techniques to enable the practitioner to absorb whole subjects very rapidly, and to understand very complex subjects on first reading, as well as remembering whatever has been read. Like many magic manuscripts this work was attributed to famous individuals including Solomon (who reputedly received the book directly from God via the angel Pamphilius), which was translated into Greek by the magician Apollonius of Tyana, along with input from Euclid of Thebes, the father of Honorius of Thebes the author of The Sworn Book of Honorius (Liber Juratus) and Mani, the prophet. Solomonic grimoires are concerned with the evocation of spirits or demons, but the Ars Notoria stands alone as angel magic concerned only with memory and the ability to understand and absorb whole subjects rapidly, making it a veritable student's grimoire, a key to obtaining knowledge rapidly. Despite its popularity and enduring history the Ars Notoria has never been printed in its complete form. After its early Latin appearance there was only one incomplete English translation by Robert Turner in 1657, and that omitted the most vital component for its operation, the notae, a set of complex pictorial illustrations, without which the system just does not work. It also abbreviated most of the orations/invocations. The present edition contains all the notae matched with all the complete invocations/orations, and instructions for their use.