From the airport to downtown
On arrival at Stavanger airport Sola, proceed through customs and into the arrivals hall (~20 mins). Immediately outside the arrivals hall, find the airport shuttle "Flybussen". It is the least complicated way to get to town. It leaves approximately every 20-30 minutes and the trip takes about half an hour. The one-way ticket costs 136 NOK and the return ticket costs 205 NOK if bought on the Flybussen webpage. The ticket can also be bought by cash or credit card on the bus by paying an extra fee.
The driver will speak English and will be able to inform you of when to get off for your hotel.
Your Flybussen ticket entitles you to one change onto the local buses.
From the airport to the UiS campus in the working days.
The instructions are essentially those to go to Stavanger center. The difference is that only the Flybussen buses going to Stavanger center "via SUS og UIS" cross the campus. The most convenient stop is UiS Vest. The buses leave the airport every 20-30 minutes.
From the airport to the UiS campus during weekends
Flybussen does not go to the University campus in the weekends. If you are in a hurry, taxi is the fastest option. Ask the driver to take you to "University of Stavanger, Main Building". Journey time is about 20 minutes and the cost is very approximately 400 NOK.
Otherwise, googlemaps shows the public trasport options to the campus. The airport, campus and city center are all within the same transport area so that the 1-zone fare suffices. The tickets can be bought via the Kolumbus app at the prices indicated here. The single journey ticket can be bought directly from the bus driver only by cash with an extra fee of 20 NOK.