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This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory. A selection of exercises follows each chapter, and proofs to most of the theorems are included. The text assumes a basic knowledge of functional analysis, and a bibliography allows researchers and students to continue in the direction of their individual interests.