The network layer is responsible for packet routing between different networks. It determines the best path for packet transmission and places the source and destination IP addresses in packet headers. Common routing algorithms include shortest path routing, flooding, distance vector routing, and link state routing. Shortest path routing finds the lowest cost path using algorithms like Dijkstra's. Flooding transmits packets to all neighbors, creating duplicates. Distance vector and link state routing adapt to network changes by exchanging routing information between routers.