This book, a result of nineteen years’ lectures on the Calculus of Finite Differences, Probability, and Mathematical Statistics in the Budapest University of Technical and Economical Sciences, and based on the venerable works of Stirling, Euler and Boole, has been written especially for practical use, with the object of shortening and facilitating the labours of the Computer. With this aim in view, some of the old and neglected, though useful, methods have been utilized and further developed: as for instance Stirling’s methods of summation, Boole’s symbolical methods, and Laplace’s method of Generating Functions, which last is especially helpful for the resolution of equations of partial differences.