A computer network connects multiple computers together allowing sharing of resources. There are two main types: local area networks (LANs) covering a small area like a school, and wide area networks (WANs) spanning large geographical areas like the internet. Network topologies determine how devices are physically connected - a bus network uses one cable, a ring network forms a continuous loop, and a star network connects each device to a central hub/switch. Networks provide advantages like shared printing and internet access but also have costs and potential single points of failure.