This extensive selection of William Feller's scientific papers shows the breadth of his oeuvre as well as the historical development of his scientific interests. Six seminal papers - originally written in German - on the central limit theorem, the law of large numbers, the foundations of probability theory, stochastic processes and mathematical biology are now, for the first time, available in English. The material is accompanied by detailed scholarly comments on Feller's work and its impact, a complete bibliography, a list of his PhD students as well as a biographic sketch of his life with a sample of pictures from Feller's family album. Volume I covers the early years 1928-1949, featuring the celebrated Lindeberg-Feller Central Limit Theorem, while Volume II contains papers from 1950-1971 when the theory of Feller processes and boundaries had been developed. William Feller was one of the leading mathematicians in the development of probability theory in the 20th cent ury. His work continues to be highly influential, in particular in the theory of stochastic processes, limit theorems and applications of mathematics to biology. These volumes will be of value to all those interested in probability theory, analysis, mathematical biology and the history of mathematics.