There is a rover ticket for use in Luxembourg that is of astonishing value at just €4/day. The Dagesbilljee, or “day ticket” covers travel on all trains and buses throughout the Grand Duchy. If you intend to spend longer there, you can buy a book of five tickets for €16 (essentially, buying four days’ travel and giving you the fifth for free).
These tickets can be purchased at the machine at the bus stop outside the front of the airport, or at ticket machines at railway stations. They can also be bought from the grippers on the trains, but that incurs an extra €1 charge.