There is a growing interest in discovery of internet topology at the interface level. A new generation of highly distributed measurement systems is currently being deployed. Unfortunately, prior to this thesis, the research community has not examined the problem of how to perform such measurements efficiently and in a network- friendly manner. In this book, we make several contributions toward that end. First, we show that standard topology discovery methods are quite inefficient, repeatedly probing the same interfaces. This is a concern, because when scaled up, such methods will generate so much traffic that they will begin to resemble DDoS attacks. As it is not unusual for a route tracing monitor to operate in isolation, we next propose and evaluate strategies for reducing redundancy within a single monitor. We third propose and evaluate Doubletree, a cooperative algorithm that reduces redundancy simultaneously on routers and end systems. Finally, we also provide a generalization of Bloom filters, called retouched Bloom filters, that permits false negatives in addition to false positives and allows a trade-off between the two.