This book focuses on the analysis and design of advanced techniques for on-line automatic computational monitoring of pipelines and pipe networks. It discusses how to improve the systems' security considering mathematical models of the flow, historical flow rate and pressure data, with the main goal of reducing the number of sensors installed along a pipeline. The techniques presented in the book have been implemented in digital systems to enhance the abilities of the pipeline network's operators in recognizing anomalies. A real leak scenario in a Mexican water pipeline is used to illustrate the benefits of these techniques in locating the position of a leak. Intended for an interdisciplinary audience, the book addresses researchers and professionals in the areas of mechanical, civil and control engineering. It covers topics on fluid mechanics, instrumentation, automatic control, signal processing, computing, construction and diagnostic technologies.