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This introduction to "probability theory" can be used, at the initial graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course. It should be useful for students and teachers in related areas such as finance theory (economics), electrical engineering and operations research. The text covers the essentials with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it should bring them from a starting knowledge of the subject to a knowledge of the basics of Martingale theory. After learning probability theory from this text, the student should be ready to continue with the study of more advanced topics, such as Brownian motion and Ito calculus, or statistical inference.