A hub works on layer 1, the physical layer. It's more or less a splitter, and also amplifies the signal allowing for extending the domain. All connections on a hub are on the same collision domain.
A switch is layer 2, Datalink/Ethernet layer. A switch will remember the MAC addy of each port and determine which IP belongs to which MAC and store that in a built in table. Each port is a seperate collision domain, allowing full duplex between the port and the device on the other end. There are a number of different types of switches, but that is beyond the scope of this.
A router is typically layer 3, but some can go all the way to layer 7. As yodapaul said.
Imma go back to being stupid again.
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Get off your fuckin cross. We need the fuckin space to nail the next fool martyr.
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