Providing the first truly comprehensive overview of Network Tomography - a novel network monitoring approach that makes use of inference techniques to reconstruct the internal network state from external vantage points - this rigorous yet accessible treatment of the fundamental theory and algorithms of network tomography covers the most prominent results demonstrated on real-world data, including identifiability conditions, measurement design algorithms, and network state inference algorithms, alongside practical tools for applying these techniques to real-world network management. It describes the main types of mathematical problems, along with their solutions and properties, and emphasizes the actions that can be taken to improve the accuracy of network tomography. With proofs and derivations introduced in an accessible language for easy understanding, this is an essential resource for professional engineers, academic researchers, and graduate students in network management and network science.