A computer network connects computers to share information and resources. There are different topologies that define how computers are physically connected in a network, including bus, star, ring, and mesh. Bus topology connects all computers to a single cable but failure of the cable shuts down the whole network. Star topology connects each computer to a central hub, allowing individual failures without network shutdown. Ring topology is like a bus but with the first and last computers connected, using tokens for communication. Mesh combines star and ring for greater reliability but at higher cost. The optimal topology depends on network size and needs.