 This entry briefly describes the history and significance of Alfred North Whitehead and Bertrand Russell’s monumental but little read classic of symbolic logic, Principia Mathematica (PM), first published in 1910–1913. The content of PM is described in a section by section synopsis, stated in modernized logical notation and described following the introductory notes from each of the three volumes. The original notation is presented in a companion article of this Encyclopedia,  The Notation of Principia Mathematica.  The content of PM is described so as to facilitate a comparison with Gottlob Frege’s Basic Laws of Arithmetic which was subject to Russell’s Paradox. To avoid the paradox Whitehead and Russell introduced a complex system now called “the ramified theory of types”. After the introduction of a theory of sets, or “classes” early in the first volume, however, the system of PM can be compared with both Frege and the early development of set theory and found to contain rival accounts, free of contradiction, but differing from the now standard theories in as yet understudied ways.