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This text presents a self-contained introduction to elementary probability theory and stochastic processes with a special emphasis on their applications in science, engineering, finance, computer science, and operations research. This edition provides a completely rewritten and expanded part on probability theory. Along with additional examples, exercises, and figures, it includes new sections on time series analysis, random walks, branching processes, and spectral analysis of stationary stochastic processes. It also offers numerical discussions of examples, which replace theoretically challenging sections from the first edition.