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Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of Natural Philosophy) often referred to as simply the Principia (/ p r ɪ n ˈ s ɪ p i ə, p r ɪ n ˈ k ɪ p i ə /), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The Principia is written in Latin and comprises three volumes, and was authorized, imprimatur, by Samuel Pepys, then-President of the Royal Society on 5 July 1686 and first published in 1687.

The Principia is considered one of the most important works in the history of science. The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of Mathematical Principles of Natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses." The French scientist Joseph-Louis Lagrange described it as "the greatest production of a human mind", and French polymath Pierre-Simon Laplace stated that "The Principia is pre-eminent above any other production of human genius". Newton's work has also been called the "greatest scientific work in history", and the "supreme expression in human thought of the mind's ability to hold the universe fixed as an object of contemplation".

A more recent assessment has been that while acceptance of Newton's laws was not immediate, by the end of the century after publication in 1687, "no one could deny that a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally".

The Principia forms a mathematical foundation for the theory of classical mechanics. Among other achievements, it explains Johannes Kepler 's laws of planetary motion, which Kepler had first obtained empirically. In formulating his physical laws, Newton developed and used mathematical methods now included in the field of calculus, expressing them in the form of geometric propositions about "vanishingly small" shapes. In a revised conclusion to the Principia (), Newton emphasized the empirical nature of the work with the expression Hypotheses non fingo ("I frame/feign no hypotheses").

After annotating and correcting his personal copy of the first edition, Newton published two further editions, during 1713 with errors of the 1687 corrected, and an improved version of 1726.