Riding your bike
You should have functioning brakes. Lights are required at night. The police is authorized to stop and fine you if you do not have lights. Also, bicyclists are supposed to ride their bikes on the bicycle lanes, if there are no available, drive on the regular street. Even though many people do it, you legally shouldn't ride your bike on the sidewalk. The police might fine you for that as well.
Buying a bike
Many students go to university by bike – if you want to follow this summer trend or if you want to make a weekend excursion to the Netherlands, you might consider buying a 2nd hand bicycle.
There is a monthly bicycle market (Aachener Fahrradrad) in front of the Kármán-Auditorium always on the 2nd Saturday of each month. http://www.aachener-fahrradmarkt.com. The bicycles tend to be a little pricey, even though they are still much cheaper than the high end bikes offered in most bike shops.
ebay notice board http://kleinanzeigen.ebay.de/anzeigen/s-fahrraeder/aachen/c217l1921 You might have to be quick for this one.
Another great place to get good quality, second hand bicycles is the bike shop of “WABe e.V.”, a bike recycling place located near Kaiserplatz.