Although the words “stochastic” and “stochastics” are frequently used, their exact meaning may not be generally known. The Greek noun stochos means target, aim, or guess. Stochastikos is a person who is skilful in predicting. From this point of view, the title ‘Ars conjectandi’ of the famous book by Jacob Bernoulli has the Greek equivalent ‘στοχαστικη τεχνη’ (stochastic techniques). Formerly, the word “stochastic” was used mainly in the phrase “stochastic process”. Today one feels that “stochastic” means more than only “random”. The book contains contributions devoted to the problem of how to define the science of stochastics. The articles are revised and updated versions of lectures delivered at the symposium “Defining the Science of Stochastics”, which took place in Germany in October 2000. The publication is divided into three parts, each one having three papers. The first part describes the present state of statistics and probability theory in comparison to the science of stochastics. The second part deals with randomness, contingency, and white noise. The third part is devoted to stochastics in public education. The authors of individual contributions are S. Kotz, U. Herkenrath, V. Kalashnikov, J. Kohlas, C. S. Calude, T. Hida, M. Dumitrescu, and E. von Collani (2×). The authors emphasize history and nature of statistical science and propose to establish “Stochastics” as an independent, mathematically based exact science, which investigates the inherent variability exhibited by any real phenomenon. A great variety of topics in the published papers, reflects the fast growing diversification of statistical sciences. It might be that the reader finds some of them to be too far from his/her specialization, but everybody will find some contributions interesting and stimulating. In Biographical Notes, on p. 215, one reads that Thomas Bayes lived 1702-1761. According to the inscription on his tomb in Bunhill Field cemetery in London, he died on April 7, 1761, at age of 59. Some authors introduce that he was probably born in 1701.