By bus from the airport to the Department of Philosophy KGW:

The bus stop is right in front of the airport exit. Just cross the street with the waiting cabs. Bus tickets can be bought from the bus driver or from the vending machine at the bus stop. The easiest and fastest way to get to the city center is to take line 10 in the direction of Sam Lankessiedlung. The timetable is available at  https://fahrplan.salzburg-verkehr.at/. Get off at the Herbert -v.-Karajan Platz stop. From the stop, walk to the Department of Philosophy at Franziskanergasse 1. You can see the route described on the map:

By bus from the main train station to the Department of Philosophy KGW:

When you leave the main train station, the bus stops are on the left in front of you. You can either take line 3 in the direction of Salzburg Süd S-Bahn, or line 6 in the direction of Parsch L.-Schmederer-Platz or line 5 in the direction of Birkensiedlung/Untersbergbahn. The buses leave every ten minutes. Tickets can be purchased from the bus driver or from the ticket machine at the bus stop. All lines take you directly to the bus stop Rathaus. Get off there and you will see the route described on the map: