We develop Methane, a system to synthesize provably-correct configurations for large, evolving networks from high-level specifications of topology, routing policy, and fault-tolerance requirements. It is based on new abstractions for capturing parameterized network topologies and their evolution, and algorithms to analyze the impact of topology and routing policy on fault tolerance. Our algorithms operate entirely on abstract topologies and guarantee correctness for all its concrete instantiations. Methane also guarantees that minimal changes to existing device configurations are required when the network evolves to add or remove devices and links. Our experiments with real-world topologies and policies show that our abstractions and algorithms are effective and that, for large networks, Methane synthesizes configurations two orders of magnitude faster than systems that operate over concrete topologies.