At the time the first volume of this book was written (between 1941 and 1948) the interest in probability was not yet widespread. Teaching was on a very limited scale and topics such as Markov chains, which are now extensively used in several disciplines, were highly specialized chapters of pure mathematics. The first volume may therefore be likened to an all-purpose travel guide to a strange country. To describe the nature of probability it had to stress the mathematical content of the theory as well as the surprising variety of potential applications. It was predicted that the ensuing fluctuations in the level of difficulty would limit the usefulness of the book. In reality it is widely used even today, when its novelty has worn off and its attitude and material are available in newer books written for special purposes. The book seems even to acquire new friends. The fact that laymen are not deterred by passages which proved difficult to students of mathematics shows that the level of difficulty cannot be measured objectively; it depends on the type of information one seeks and the details one is prepared to skip. The traveler often has the choice between climbing a peak or using a cable car.

In view of this success the second volume is written in the same style. It involves harder mathematics, but most of the text can be read on different levels. The handling of measure theory may illustrate this point. Chapter IV contains an informal introduction to the basic ideas of measure theory and the conceptual foundations of probability. The same chapter lists the few facts of measure theory used in the subsequent chapters to formulate analytical theorems in their simplest form and to avoid futile discussions of regularity conditions. The main function of measure theory in this connection is to justify formal operations and passages to the limit that would never be questioned by a non-mathematician. Readers interested primarily in practical results will therefore not feel any need for measure theory.