Part 1 gives historical background and discussion of some general features of Newtonian dynamics. Part 2 is the heart of the book: Newton's proofs of Kepler's laws, and of course especially the theorem that planets move in ellipses around the sun. Brackenridge goes through Newton's proofs step by step in great detail. It is quite hopeless for a modern reader to follow these proofs in the Principia, but, as one would expect, with a guide like this it is easy to see the general strategy and follow the steps. But Newton's proofs use a few nontrivial theorems from classical geometry. These were surely known to Newton's readers, but they certainly are not today. Brackenridge doesn't prove these theorems, so if we really want to understand Newton's proof of the law of ellipses (which is "the goal of the book"; p. vii), then we are forced to go look up serious theorems in Euclid and Apollonius. Part 3 discusses Newton's published and unpublished alternative approaches to the problems of planetary motion. Brackenridge argues that the first edition of the Principia is the clearest (in the later editions insights are "hidden in a labyrinth"; p. 209); a translation of the relevant parts is given here as an appendix. It was only in the later editions that Newton added the curvaturesque arguments leading to the "the same otherwise" alternative proofs that we find in the common third edition.