New concise edition with a new introduction, abridged for the modern reader. The Principia. Mathematical Principles of Natural Philosophy is one of the most important scientific works ever to have been written and has had a profound impact on modern science. Consisting of three separate books, the Principia states Newton’s laws of motion and Newton’s law of universal gravitation. Understanding and acceptance of these theories was not immediate, however by the end of the seventeenth century no one could deny that Newton had far exceeded all previous works and revolutionised scientific thinking. The FLAME TREE Foundations series features core publications which together have shaped the cultural landscape of the modern world, with cutting-edge research distilled into pocket guides designed to be both accessible and informative.

This monograph describes the different formulations of Einstein's General Theory of Relativity. Unlike traditional treatments, Cartan's geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. The book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.