Assessing and predicting internal network performance is of fundamental importance in problems ranging from routing optimization to anomaly detection. The problem of estimating internal network structure and link-level performance from end-to-end measurements is called network tomography. This thesis investigates the general network tomography problem involving multiple sources and receivers, building on existing single source techniques. Using multiple sources potentially provides a more accurate and refined characterization of the internal network. The general network tomography problem is decomposed into a set of smaller components, each involving just two sources and two receivers. A novel measurement procedure is proposed which utilizes a packet arrival order metric to classify two-source, two-receiver topologies according to their associated model-order. Then a decision-theoretic framework is developed, enabling the joint characterization of topology and internal performance. A statistical test is designed which provides a quantification of the tradeoff between network topology complexity and network performance estimation.