Networks of computer systems, distribution systems, and telecommunication systems play an increasingly important role in our lives. This book is concerned with analysing and assessing the reliability of such networks whose components are prone to possible failure. The field of network reliability has expanded rapidly to provide various mathematical models and computational procedures. In this book the emphasis is on identifying a number of algebraic structures that serve to unify the study of networks, and to suggest new techniques and procedures for analysing the probabilistic behaviour of networks. Consequently, amongst the topics covered are pseudopolynomial algorithms, lattice structures, spaces of polynomials, reliability covering problems, and stochastic path problems. The result is a book which will be an invaluable account of the subject for all mathematicians, computer scientists, reliability engineers, and operations researchers whose work touches on network reliability.