A Huguenot exile in England, the French mathematician Abraham de Moivre (1667–1754) formed friendships with such luminaries as Edmond Halley and Isaac Newton. Making his living from private tuition, he became a fellow of the Royal Society in 1697 and published papers on a range of topics. Probability theory had been pioneered by Pascal, Fermat and Huygens, with further development by the Bernoullis. Originally published in 1718, The Doctrine of Chances was the first English textbook on the new science and so influential that for a time the whole subject was known by the title of the work. Reissued here is the revised and expanded 1738 second edition which contains the remarkable discovery that when a coin is tossed many times, the binomial distribution may be approximated by the normal distribution. This version of the central limit theorem stands as one of de Moivre's most significant contributions to mathematics.