As cloud computing, artificial intelligence infrastructure, and internet services continue to grow, it becomes increasingly important to monitor the large networked systems that support communication, commerce, education, health, and science. These systems include massive collections of servers, network devices, storage services, and software components that must work together reliably and efficiently. However, the data generated about network traffic, resource usage, and failures can be too large to analyze in full, especially when operators need answers in real time. This project develops an approximation-first approach to telemetry for hyperscale networked systems, using compact, informative data summaries to answer important monitoring questions quickly while greatly reducing cost and overhead. The project establishes an end-to-end approximation-first telemetry architecture for hyperscale networks through four research thrusts. The first develops mergeable summaries that can be created on end hosts and networked devices while tracking uncertainty. The second develops low-latency aggregation and query methods that answer telemetry questions directly from these summaries. The third develops learning-guided compression for long-term telemetry storage using both lossy and lossless approaches. The fourth creates a management engine that maps user goals for accuracy, responsiveness, and cost into efficient telemetry configurations. Together, these thrusts advance telemetry systems, networked systems, and large-scale distributed computing. The project's cost-effective telemetry can help operators detect network anomalies, bottlenecks, failures, and attacks more quickly while lowering the compute, storage, and energy required for monitoring. The project will also create educational materials and hands-on learning opportunities in networking, cloud computing, and systems, and will release open-source software to support researchers, students, and practitioners buil