networking - Differences between a modem, a wireless access point and a router

Can anyone explain the differences between a modem, a wireless access point, and a router?

What functions do they share and which functions uniquely characterize them?

Answer

Modem - Box from your ISP that connects to the internet. It actually connects to the phone line or the coaxial cable or whatever physical line you have. It normally has at least an ethernet connection, sometimes a USB as well.

Router - Box that connects to the modem and allows multiple devices to use that internet connection at the same time. It also lets the devices talk to each other (so you can transfer files in your house or whatever). Can be wired, wireless, or both.

Wireless Access Point - Attaches to a router and allows wifi connections to the network.