A student of Trinity College and a member of the Cambridge Apostles, William Kingdon Clifford (1845-79) graduated as second wrangler in the mathematical tripos, became a professor of applied mathematics at University College London in 1871, and was elected a fellow of the Royal Society in 1874. The present work was begun by Clifford during a remarkably productive period of ill health, yet it remained unfinished at his death. The statistician and philosopher of science Karl Pearson (1857-1936) was invited to edit and complete the work, finally publishing it in 1885. It tackles five of the most fundamental areas of mathematics - number, space, quantity, position and motion - explaining each one in the most basic terms, as well as deriving several original results. Also demonstrating the rationale behind these five concepts, the book particularly pleased a later Cambridge mathematician, Bertrand Russell, who read it as a teenager.