This book is an introductory textbook on probability theory and its applications. Basic concepts such as probability measure, random variable, distribution, and expectation are fully treated without technical complications. Both the discrete and continuous cases are covered, but only the elements of calculus are used in the latter case. The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. Special topics include: combinatorial problems, urn schemes, Poisson processes, random walks, and Markov chains. Problems and solutions are provided at the end of each chapter. Its elementary nature and conciseness make this a useful text not only for mathematics majors, but also for students in engineering and the physical, biological, and social sciences. This edition adds two chapters covering introductory material on mathematical finance as well as expansions on stable laws and martingales. Foundational elements of modern portfolio and option pricing theories are presented in a detailed and rigorous manner. This approach distinguishes this text from others, which are either too advanced mathematically or cover significantly more finance topics at the expense of mathematical rigor. Farid AitSahlia is currently a Senior Scientist with DemandTec, where he develops econometric and optimization methods for demand based pricing models. He is also a visiting scholar in the department of Statistics at Stanford University, where he obtained his PhD in Operations Research. Farid AitSahlia has published several papers on option pricing and has previously taught mathematical finance at Cornell University. Prior to joining DemandTec, he worked at Financial Engines, where he developed mathematical finance models
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