This volume presents an overview of mathematical methods used in queuing theory, and various examples of solutions of problems using these methods are given. Many of the topics considered are not traditional, and include general Markov processes, test functions, coupling methods, probability metrics, continuity of queues, quantitative estimates in continuity, convergence rate to the stationary state and limit theorems for the first occurrence times. Much attention is also devoted to the modern theory of regenerative processes. Each chapter concludes with problems and comments on the literature cited. For researchers and graduate students in applied probability, operations research and computer science.