This book is devoted to the probabilistic description of a network in the process of its destruction, i.e. removal of its components (links, nodes) appearing as a result of technical failures, natural disasters or intentional attacks . It is focused on a practical approach to network reliability, based on application of Monte Carlo methodology to numerical evaluation of network most important structural parameters. This allows to obtain a probabilistic description of the network in the process of its destruction, to identify most important network components and to develop efficient heuristic algorithms for network optimal design. The methodology works with satisfactory accuracy and efficiency for small -to-medium size networks.