If you come from Germany or Europe, using the train may be an option. There are (direct) high-speed train links to Stuttgart from many German cities and from several European destination, including Paris and Vienna.
When arriving at Stuttgart Hauptbahnhof (Stuttgart main station), follow the signs to the S-Bahn station (green S symbol, see S-Bahn Stuttgart).
Trains to University normally leave from track 101, which is underground. Take one of the trains S1, S2, or S3 with destinations Böblingen, Filderstadt, Flughafen/Messe, Herrenberg, or Vaihingen.
Exit the train at the stop Stuttgart Universität (University) and use the exit Universitätszentrum. The S-Bahn ride to University takes about 10 minutes.
You may plan your (international) rail trip to Stuttgart online: