If you have a connection to the Internet using DSL or cable then you have a router, although it may be called something different. These boxes are small and will only have a few connections also.
Usually, you will see them called DSL modems or cable modems. They really are not modems. Modems convert digital signals to analog signals. Your computer uses digital signals, and telephone used/uses analog. With dialup, you have a modem. People got used to the box between the telephone line and the computer being a modem so they refer to the box between the cable or DSL line and the computer as a modem. In the case of DSL and cable, you have a digital signal on the cable or DSL (the D in DSL is digital) and the computer is still digital, so it is not a modem technically.
The DSL or cable modem is really a router because it is connecting your network. Your computers at your house, one or more, is a network, and you are connecting to your ISP (cable or DSL) network. A router connects the networks together. You can do limited rule setting in these personal routers.
Special note : This is the 100th question answer article I have done, and I continue to amaze myself weekly on finding another subject to tell my readers about. I appreciate the newspapers who carry this article, and especially the Swainsboro Forest Blade for giving me the original opportunity. To the Blade, the Messenger and the Catoosa News and all my readers thank you for the encouragement over the last two years. There is still plenty of material for the next 100.
Send your questions to Dwight Watt at email@example.com. He teaches at a technical college in northwest Georgia and does consulting work for businesses and individuals. His website is www.dwightwatt.com.