Computer networks allow computers and devices to connect and share resources. There are three main types of networks - local area networks (LANs) which connect devices in a small geographic area like a home or office, metropolitan area networks (MANs) which connect devices in a city or town, and wide area networks (WANs) which connect devices across large geographic areas or even globally like the internet. Network topology refers to how computers are arranged and connected in a network, with common topologies being bus, star, and ring configurations.