Any stochastic model involves random data and their transformations and of primary interest are the corresponding probability distributions. Since explicit distributions of the transformed data are only rarely available, we need 'good' approximations. From a computational point of view these are hard problems. There are several methods for approximate calculations which are either with a limited range of applicability, or they do not produce results of a good accuracy. There is an opinion that in some sense the statistical theory and practice have been saved because of the saddlepoint method. Today this is perhaps the most powerful method used in statistical theory and practice. The theory behind this method is quite complicated and involves different branches of mathematics. The author's twofold goal with writing this book looks ambitious. First, he wants to tell the reader what is the essence of the saddlepoint method and to show how it works when solving specific and general problems. Second, he wants to write in an 'understandable language'. For this reviewer the author is successful.
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