The birth of the Principia may be traced back to a discussion in 1684 at the Royal Society. Astronomer Edmund Halley and architect Sir Christopher Wren suspected that there was an inverse square relation governing celestial motions based on Kepler's Third Law of elliptical orbits, but no one could prove it. They brought the question before Newton's arch rival Robert Hooke, who claimed that he could prove the inverse square law and all three of Kepler's laws. His claim was met with scepticism, and Wren offered a forty-shilling book as a prize for the correct proof within a two-month limit. Hooke failed to produce the calculation, and Halley travelled to Cambridge to ask for Newton's opinion. Newton responded with a typical lack of interest in work that he had already completed, that he had already solved the problem years before. He could not find the calculation among his papers and promised to send Halley a proof. Halley, suspecting the same bogus claim he had received from Hooke, left frustrated and returned to London. Three months later he received a nine page treatise from Newton, written in Latin, De Motu Corporum, or On the Motions of Bodies in Orbit. In it, Newton offers the correct proof of Kepler's laws in terms of an inverse square law of gravitation and his three laws of motion. Halley suggested publication, but Newton, reluctant to appear in print, refused. At Halley's insistence, Newton finally began writing and, with typical thoroughness, worked for 18 months revising and rewriting the short paper until it grew into three volumes. The Royal Society, having exhausted available funds on an extravagant edition of De Historia Piscium, or The History of Fishes, could not pay for the publication and so it was at Edmund Halley's expense that Philosophi?Naturalis Principia Mathematica was finally published.

The Mathematical Principles of Natural Philosophy, or The Principia as it came to be commonly known, begins with the solid foundation on which the three books rest. Newton begins by defining the concepts of mass, motion (momentum), and three types of forces: inertial, impressed and centripetal. He also gives his definitions of absolute time, space, and motion, offering evidence for the existence of absolute space and motion in his famous "bucket experiment". These absolute concepts provoked great criticism from philosophers Leibnitz, Berkeley, and others, including Ernst Mach centuries later. The three Laws of Motion are proposed, with consequences derived from them. The remainder of The Principia continues in rigorously logical Euclidean fashion in the form of propositions, lemmas, corollaries and scholia. Book One, Of The Motion of Bodies, applies the laws of motion to the behaviour of bodies in various orbits. Book Two continues with the motion of resisted bodies in fluids, and with the behaviour of fluids themselves. In the Third Book, The System of the World, Newton applies the Law of Universal Gravitation to the motion of planets, moons and comets within the Solar System. He explains a diversity of phenomena from this unifying concept, including the behaviour of Earth's tides, the precession of the equinoxes, and the irregularities in the moon's orbit.

The Principia brought Newton fame, publicity, and financial security. It established him, at the age of 45, as one of the greatest scientists in history.