From the Foreword by Sir Joseph Needham: "As will be seen from the present book, mathematics had a very great development in ancient China. This was perhaps to be expected in view of the advanced nature of their astronomy. If China developed no Euclidean deductive geometry, there was plenty of empirical geometry there ...the Chinese always preferred algebraic methods; and indeed by the thirteenth century AD, they were the best algebraists in the world." The mathematical developments in China over a period of more than 2000 years are presented in more detail than has previously been available in English. Horner's method, Bezout's theorem, and other important results were obtained centuries earlier than they were in the West. The reader will find these and other familiar results presented in a very different context from the Western Euclidean framework. In Chinese mathematics the emphasis is on algorithms rather than proofs. With the assistance of the surviving junior author, Du Shiran, the translators have retained the Chinese point of view while supplementing the text with short explanatory comments and references to all the available, relevant material written in western languages (chiefly English). Brief appendices on the history and language of China, together with extensive bibliography, should make this a useful source book.