This book presents an introduction to the theory of large deviations. Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition includes new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications have been sharpened, new exercises added, and the bibliography updated.