Principia Mathematica was first published in 1910-13; this is the ninth impression of the second edition of 1925-7. The Principia has long been recognised as one of the intellectual landmarks of the century. It was the first book to show clearly the close relationship between mathematics and formal logic. Starting from a minimal number of axioms, Whitehead and Russell display the structure of both kinds of thought. No other book has had such an influence on the subsequent history of mathematical philosophy.
Amazon.com Review Could it be true that Whitehead and Russell's Principia Mathematica is the most influential book written in the 20th century? Ask any mathematician or philosopher — or anyone who understands the impact these fields have had on modern thinking — and you'll get a short answer: yes. Their goal, to set mathematics on a firm logical foundation, was revolutionary, and their tools and rigor continue to influence modern professionals. Using Peano's symbolic logic, they formalized axioms and produced theorems (including the famous "1 + 1 = 2") in orderings, continuous functions, and other areas of mathematics.
Although the Principia is far from comprehensive, Whitehead and Russell's method and program captivate their readers. The audacity to hope to formalize all of mathematics logically was inspirational and helped to give great boosts to math and logical philosophy. Though G?del proved in 1931 that any such program is doomed to incompleteness, the tools found in and developed from the three volumes helped build the atomic bomb and the Internet. It may not be summer-vacation reading (for most), but Principia Mathematica will reward the dedicated student with a deeper understanding of how we got here. — Rob Lightner