Brewing in a rented space/place. Can you brew beer in an apt? I could let it age in my closet, or the balcony storage shed.
The only concern I'd see right away would be making sure you don't lose your deposit if you have a blow out during fermentation and beer sprays all around.  I've not done it in an apartment, but I just use my stove and a wort chiller that attaches to my sink, so there isn't anything in that process that would be a problem in an apartment.

I suppose if you want to use a big propane burner for boiling the wort you might need to check if such things are permitted at your property.  If they don't allow BBQs you probably couldn't use that type of burner.  If you've got the time you should be able to do it on most stove tops though.  And more time to brew means more time to enjoy previously brewed after all!

For the fermentation, ideally you'll want a dark place that's reasonably temperature controlled, but if your apartment has its temps in a reasonable range you could probably make it work without a special fermentation chamber--which you could also likely buy or make if you care enough to.