The whole Principia is very large: It is said that the book is famous for taking a thousand pages to prove that 1+1=2. As the preface stresses, the proofs are excruciatingly detailed so to remove the chance of an unstated premise being used in a proof. The goal of Principia was to put forward a set of very basic notions, and show that they and they alone are sufficient for the whole Mathematics. If Principia were to be published today, all the proofs would be relegated to a Supplement (or a theorem prover). What important are the basic notions and the set up -- most of which is explained in the Preface and Chapter 1. These following are a few notes taken while reading Chapter 1 of Principia, with several comments very kindly given by Jacques Carette. Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Cambridge: University Press, 1910- http://name.umdl.umich.edu/AAT3201.0001.001 The full scanned text, many thanks to The University of Michigan Historical Mathematics Collection Linsky, Bernard. The Notation in Principia Mathematica The Stanford Encyclopedia of Philosophy (Summer 2026 Edition), Edward N. Zalta & Uri Nodelman (eds.) https://plato.stanford.edu/archives/sum2026/entries/pm-notation/ p≡q we shall have f(p)≡f(q)''. Here f(p) is a proposition that includes another proposition p. In modern terms, we would call f a context and denote by C[], and say that if C[p]≡C[q], which is the familiar statement of a referential transparent context. The page then shows an example of a non-referentially transparent context ``A believes p'': a proposition whose meaning varies when …the definitions are not part of our subject, but are, strictly speaking, mere typographical conveniences.… In spite of the fact that definitions are theoretically superfluous, it is nevertheless true that they often convey more important information than is contained in the propositions in which they are used. … The collection of definitions embodies our choice of subjects...