Do you need a router if you have a modem?

A modem just connects to your isp so that you can connect to the internet. Something that is just a modem will likely only have a port for the phoneline and an ethernet port. If you only have one computer/device to connect this is fine, if you have multiple devices to connect or want wifi you need a router to plug into the modem. A lot of the time the modem your isp gives you will have a cheap wifi router in it already.

No if you connect your computer to the modem using a LAN cable. If you go wireless on the internet, you do need a router for directing your communication from the modem to the computer.

In order for devices on the network to connect to the Internet, the router must be connected to a modem. Therefore, most routers have a specific Ethernet port that is designed to connect to the Ethernet port of a cable or DSL modem.

Modulation & Demodulation, modem only allow you to send data over Telephone system it can not allow you to reroute your data so if it use on a single computer so no need to route because computer also a good router if u want distribute your modem connection then you need a router. 

without a modem your router will only allow you to connect to a LAN (local area network).The modem is your connection to the internet .