Routing protocols exchange network, routes, and metric information between routers to help find optimal routes as fast as possible. Routers use the information provided by routing protocols to build their routing tables for each routed protocol to keep track of paths to networks.
Most routers support multiple routing protocols but the most popular are:
Routing Information Protocol (RIP)
Enhanced Interior Gateway Routing Protocol (EIGRP)
Open Shortest Path First (OSPF)
Intermediate System To Intermediate System(IS-IS)
Routing protocols use metrics ( metric being a measure of how reliable a route is) to make their routing decisions. Each routing protocol uses different criteria to work out the metric.