The late Alexander J. Khinchin was born in Russia in 1894. One of the founders of the Soviet school of probability theory, Khinchin was made a full professor at Moscow University in 1922 and held that position until his death. His teaching skill is discernible in the clear and straightforward presentation of his subject. Designed for use as an expository text in the university curriculum, the book is basically of an elementary nature, the author confining his attention to con­ tinued fractions with positive-integral elements. The essentials needed for applications in probability theory, mechanics, and, especially, num­ ber theory are given and the real number system is constructed from continued fractions. The last chapter is somewhat more advanced and deals with the metric, or probability, theory of continued fractions. This first English translation is based on the third edition of the textwhich was issued in 1961.