This paper has the aim to provide a general view of the so called Jesuit Edition (hereafter JE) of Newton's Philosophiae Naturalis Principia Mathematica (1739-1742). This edition was conceived to explain all Newton's methods through an apparatus of notes and commentaries. Every Newton's proposition is annotated. Because of this, the text--in four volumes--is one of the most important document to understand Newton's way of reasoning. This edition is well known, but systematic works on it are still missing. We are going to fill this gap by means of a project exposed in the final remarks of this paper. In this paper we will: A) expound the way in which the notes and the additions to the JE were conceived by the commentators; B) provide some pieces of information about the commentators; C) summarize the most important of their notes; D) examine closely their notes as to a particularly important question: the so called "inverse problem of the central forces". KEY WORDS: Newton, Jesuit Edition, commentaries, relationships geometry-mathematics-physics, history of mathematics and physics. MATHEMATICS SUBJECT CLASSIFICATION: 01A50, 01A55, 01A85.