This book provides a rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics. The central theme of this approach is to properly imbed the random variables of interest into the framework of a finite Markov chain, and the resulting representations of the underlying distributions are compact and very amenable to further study of associated properties. The concept of finite Markov chain imbedding is systematically developed, and its utility is illustrated through practical applications to a variety of fields, including the reliability of engineering systems, hypothesis testing, quality control, and continuity measurement in the health care sector.Contents:Finite Markov Chain ImbeddingRuns and Patterns in a Sequence of Two-State TrialsRuns and Patterns in Multi-State TrialsWaiting-Time DistributionsRandom PermutationsApplicationsReadership: Graduate students and researchers in probability and statistics.Key Features:The first effort towards a complete and detailed description of the collective modes in unconventional superfluids and superconductorsMakes use of a uniquely powerful method, the path integral techniqueAccessible to students and researchers, both theorists and experimentalistsThe authors have made significant contributions to the study of collective modes in pure superfluid 3He, 3He-4He mixtures and unconventional superconductors, and of the sound phenomena in impure superfluids and superfluids in aerogel