This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (i.i.d. random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive, and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment. The second half is a collection of applications developed at AT&T Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit-switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well: basics of job allocation, rollback-based parallel simulation, assorted priority queuing models that may be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analyzed using the tools developed in the first half of the book. . Advanced undergraduate and graduate students in engineering and applied mathematics will find this book to be an invaluable introduction to the theory and a compelling collection of real engineering applications. This book will also be an excellent resource for mathematicians, researchers, and engineers.