[tomrichards14]

I get my internet at uni by conecting my laptop via ethernet to a socket in the wall.

If i plug the ethernet form the wall into an airport express, will that provide me with wireless internet?

Also, when at home, can i just plug the airport express into the mains, and not connect it, via a cable, to my wireless modem, and it will extend the range of my wireless network?

Thanks

[Lukus]

If i plug the ethernet form the wall into an airport express, will that provide me with wireless internet?

Yes

Also, when at home, can i just plug the airport express into the mains, and not connect it, via a cable, to my wireless modem, and it will extend the range of my wireless network?

Yes and no. Yes you can do it but it will depend on on weather your router/modem supports the correct protocol for extending the network.