This is a textbook and a reference book on Boolean functions, i.e. functions of binary vectors assuming at most two values 0 and 1. First, the conventional theory and its applications in computer engineering are covered. Then - revisiting and deepening the historical notation of George Boole - Boolean operators, typically NOT, AND, and OR are replaced by standard addition, subtraction, and multiplication. This is shown to be extremely useful in the stochastic theory of Boolean functions. The latter is covered at considerable depth with numerous applications mostly in the field of reliability systems theory (fault-trees etc.). In the context of fault tree evaluation several modern Boolean algorithms are discussed, and aspects of PASCAL implementations are reviewed. The book as a whole should help theoretically minded practitioners to a clearer and deeper understanding of Boolean functions and it should give numerous hints for practical numerical work via typically Boolean computer programs.