The University of Belgrade does not have a single campus, and its buildings are spread out throughout the city. For the University map see:
The Faculty of Philology is located in the city center of Belgrade, on its main pedestrian street, Knez Mihajlova. There are two entrances to the Faculty: one from Studentski trg 3 (the main entrance) and one from Knez Mihajlova Street 42.
Taxis from Belgrade Airport into City Center cost between 1500 RSD and 2000 RSD (1€=118 RSD), depending on the time (day or night), and are probably the best option if you wish to reach your destination quickly and comfortably.
For public transportation, bus line 72 itakes you from Belgrade Airport to Belgrade City Center i.e. Zeleni Venac Square (located within walking distance from the Faculty of Philology and most of the hotels in the city center). The ticket costs 89 RSD if purchased at the kiosk and 150 RSD if purchased on the bus. Bus line 72 runs from 4am till 11:40pm.
There is also a mini bus A1 taking passengers to Slavija Square (also in the city center, near Saint Sava Church). The ticket price for the mini bus is 300 RSD and can be purchased on the bus only. The mini bus A1 runs every 20 minutes from 6am till 7pm, and every 30 minutes to an hour from 7pm till 6am.
For local transportation, get a BusPlus non-personalized card for 250 RSD on a newsstand or kiosk and load it with the desired amount of credit. Fill and re-fill it on newstands and kiosks. BusPlus Cards work on all bus, tram and trolley lines. The price for one 90-minute ride within first two city zones, covering most of the city, is 89 RSD. There are no student rates available for visiting students.
Neither Uber nor Lyft operate in Serbia, but there is a CarGo app. It can be used both for local transportation and for airport transfers (booked 24h in advance).