As with many works in mathematics, the later progress of the field of symbolic logic led to numerous improvements. Work in the school of logic started by David Hilbert at Göttingen and in the Polish school of logicians led by S. Leśniewski and his most famous student, Alfred Tarski, began with correcting what they saw as defects and gaps in PM. See Kahle (2013) and Wolenski (2013). The criticisms were immediate, begun by Chwistek (1912) soon after the first volume had been published. A series of important new presentations of mathematical logic, in particular Hilbert and Ackermann (1928), Hilbert and Bernays (1934), and Kleene (1952), were adopted as text books by successive generations of logicians. As pointed out in Urquhart (2013) this lead to a slow decline in the number of references to PM in technical work in logic, as well as its gradual replacement by other texts for the Introduction to Symbolic Logic courses that soon became a staple offering of university departments of philosophy. By the 1950s PM was no longer used as a textbook, even in graduate courses. PM’s influence, then, was enormous from 1910 to 1950, with it now having the status of a recognized classic that is unfamiliar to students of logic, and even unreadable because of its superseded notation. This entry, together with the entry on   the notation in Principia Mathematica,  are intended to make the contributions of this monumental work available, and to enable further research on some of the ideas hidden in those three long volumes.