Parking space in Maastricht is very scarce and expensive. If you have a car and you live in an area of Maastricht in which parking charges apply, you can apply for a parking permit on www.maastricht.nl.
If you live outside of Maastricht and travel to and from the city each day, it is best to use public transport as much as possible. If you are a student at Maastricht University and you want to drive to the University, you can park your car free of charge 24/7 at the University site in Randwyck and take public transport from there.