First, it seems we cannot get rid of that dated and ambiguous subset sign, the one with the redundant underlining due to Felix Hausdorff. Mathematicians are split on this matter, partly out of respect for Hausdorff no doubt, who wrote the first definitive treatise on Set Theory. The author/editors had the opportunity of using the modern non-underlined sign instead which is inclusive of sets that are not so-called "proper" subsets. (Hausdorff's use of the simpler sign restricted its use to proper subsets alone.) Important users of the newer non-underlined subset symbol include Bourbaki, Burkhill, Dieudonne, Godement, Halmos, Jacobson, Kelley, Lang, etc, and my late mentor Howard Levi. Secondly, Bertrand Russell's tutor at Cambridge University, later collaborator in creating their monumental "Principia Mathematica," Alfred North Whitehead, is missing from PCM's Part IV: Mathematicians (biographies) who himself did both "pure" and "applied" mathematics, including an alternative relativity theory. The companion to his popular "Science and the Modern World" was his less popular yet uniquely admirable "An Introduction to Mathematics" from which I first learned what the terms "continuity" and "limit" really meant, as rigorously defined in that book. Mortimer J. Adler (of "How to Read a Book" renown) succinctly described it as a "little gem" which indeed it is. Whitehead's later eminence in philosophy only enhances his purely mathematical accomplishments. Finally, aside from these two strongly recommended Whitehead books (for beginners) prior to reading the PCM, I would also recommend the following books to be read conjointly with it, from beginning levels to the mathematically serious more advanced levels: Howard Levi, "Elements of Algebra," Fourth Edition, AMS/Chelsea; Bertrand Russell, "Introduction to Mathematical Philosophy," Routledge 1993; and Saunders Mac Lane, "Mathematics Form and Function," Springer-Verlag 1986, which nicely complements the PCM itself for mathematically mature readers. [revised/updated July 27, 2011]