Is every pilot free to choose his own route from the moment of take-off?

No, standard routes are determined, known as Standard Instrument Departure (SID) routes. In principle, aircraft operators are required to keep to these routes. Pilots are fined if they deviate from the route or if they have not obtained any instructions for this. However, because an aircraft cannot be compared with a train that runs on a track, the routes are not narrow lines. There is in fact a bandwidth within which an aircraft must remain. The official name for this is an airway. By day, airways apply for jet aircraft up to an altitude of 3,000 feet (about 900 metres) after the take-off and at night, up to an altitude of 9,000 feet (about 2,750 metres).