This chapter introduces a core design principle for federated learning (FL) based on network optimization. FL systems are modeled as networks, where each node is a device with its own data and model. Edges between nodes represent communication or statistical similarity. To keep models consistent across the network, the chapter defines generalized total variation (GTV) as a measure of model differences. This leads to generalized total variation minimization (GTVMin), a learning framework that balances local accuracy with global consistency. The chapter explains how different choices in GTVMin affect learning behavior. It discusses how to optimize GTVMin using gradient or proximal methods and when these solutions are statistically reliable. Extensions to non-parametric models are handled by comparing predictions instead of parameters. The chapter also connects GTVMin to known ideas such as convex clustering and minimum-cost flow. Overall, it moves from defining FL networks to practical algorithms, making GTVMin a flexible tool for building scalable FL systems.