Do you possibly mean Leipzig/Halle airport (LEJ) since there is no such thing like a University Leipzig/Halle?

In that case it depends on where you exactly want to go to, Halle or Wittenberg. To Halle it is a short hop by regional train (about 20 min).
To Wittenberg you will have the choice to connect via Halle or Leipzig from that regional train to another regional or high speed train (ICE). Connecting through Leipzig offers more options (ICE) but in general there is 3-4 times per hour some train. The ride takes from 55 minutes to 1:20h, depending on the type of train.
From Halle central or Wittenberg central you can take the tram (Halle) or bus to your final destination. If you need some help on the details just let me know.