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 like countries. Network topology refers to how computers are arranged and connected in a network, with common topologies including bus, star, and ring configurations.