Router is a networking device that connects different networks and selects the best path to forward packets between them. It operates at the network layer of the OSI model. Cisco is the leading router manufacturer, making 70% of the market. Routers come in different sizes for different uses - access routers for small networks, distribution routers for ISPs, and core routers for backbone networks. Static routing requires manually configuring routes, while dynamic routing uses protocols to share route information between routers automatically.