This book is an introduction to the theory and applications of large deviations, a branch of probability theory that describes the probability of rare events in terms of variational problems. By focusing the theory, in Part A of the book, on random sequences, the author succeeds in conveying the main ideas behind large deviations without a need for technicalities, thus providing a concise and accessible entry to this challenging and captivating subject. The selection of modern applications, described in Part B of the book, offers a good sample of what large deviation theory is able to achieve in various different contexts: statistical hypothesis testing, random walk in random environment, heat conduction with random sources and sinks, polymer chains, and interacting diffusions. With its 60 exercises and solutions, this book can be used as a text for graduate students who have had some exposure to mathematical analysis and measure-theoretic probability.