Gdansk is accessible by plane from most European hubs, including Frankfurt, Munich, Warsaw, Stockholm, etc.
The airport is the Gdansk Lech Walesa Airport.
From the Airport it is possible to take the PKM train to reach the city (direction Gdańsk Wrzeszcz / Gdańsk Główny).
Schematic of PKM route:
Schematic from: http://www.pkm-sa.pl/
The train station Gdańsk Strzyża is the University stop. The trip takes about 15 min, the ticket is about 10 PLN. You can buy the ticket form the conductor.