Not since Ernest Nagel\\u2019s 1939 monograph on the theory of probability has there been a comprehensive elementary survey of the philosophical problems of probablity and induction. This is an authoritative and up-to-date treatment of the subject, and yet it is relatively brief and nontechnical. Hume\\u2019s skeptical arguments regarding the justification of induction are taken as a point of departure, and a variety of traditional and contemporary ways of dealing with this problem are considered. The author then sets forth his own criteria of adequacy for interpretations of probability. Utilizing these criteria he analyzes contemporary theories of probability , as well as the older classical and subjective interpretations.