The science of probability - the systematic study of mass phenomena and repetitive events - was not fully established as such until about 1919. Nine years later, Richard von Mises, one of its pioneers, brought out the first edition of this book - what has become the classic treatment of the foundations of probability theory. The present text reproduces the most authoritative translation of the definitive 1951 German edition, which was fully revised in the light of over two decades of developments in the field. Step by step, in clear, simple language and with exceptionally well chosen examples, the author unfolds what in all likelihood is still the most comprehensive investigation ever undertaken of probablity, its relation to statistics, and its truth-finding value. Professor Richard von Mises (1883-1953) was a world-renowned mathematician, aeronautical scientist and positivist philosopher. Like all of his books, this one is rigorously logical and systematic, and at the same time thoroughly grounded in empirical evidence and practical situations.