This introduction to probability theory can be used at the level of beginning graduate students for a one-semester course in probability theory or for self-study without the benefits of a formal course; the necessary measure theory is developed in the text. It will also be useful for students and educators in related fields such as financial theory, electrical engineering, and operations research. The text addresses the essential aspects in a focused and concise manner with 28 short chapters. With only a bachelor's background in mathematics, it guides readers from a basic understanding of the subject to an understanding of the fundamentals of martingale theory. After learning probability theory from this text, the interested student will be prepared to continue studying more advanced topics such as Brownian motion and Ito calculus or statistical inference. The second edition includes some additions.