Since this is an apt, your landlord should be called and he should be the one to repair this. It sounds like your lighting is just on a separete circuit than the receptacles. What was happening when the receptacles stopped, did you plug anything in. The very first thing to look for are any GFCI receptacles. Push in the reset buttons to see if power is restored. If that doesn't do it, then power should first be verified at the breaker with a volt meter. If power is at the breaker, then you probably have a loose or broken wire at the first receptacle closest to the breaker box (meaning first receptacle on the string) Receptacles are usually daisy chained. I'm gonna guess you have receptacles that are backstabbed. This is where the wires are inserted into the little holes in the backs of the receptacles. This type of connection is notorius for loose connections. Here's a link explaining backstabbing
http://www.thisoldhouse.com/toh/know...098-9,00.html#
First open the main breaker, then pull each and every receptacle and check for backstabbing. If you find any wired this way, remove the wires from the back and wrap them around the screws on the sides. This should really be done by an electrician since you're renting so be careful. Here's a link that'll show you how
http://www.danswiringpage.com/recepts_gfi.htm