Arrival by Train
Take the train to station "Hamburg-Harburg" - from there take Bus 142 to the bus stop "Technische Universität - Kasernenstraße".
If your train arrives at "Hamburg Hauptbahnhof" only - take the local train S3/S31 as described in "Arrival by public transport".
You can find the timetable for German Railways (Deutsche Bahn AG) here: https://www.bahn.de/en
Arrival by Car
Use A1, A7, B 75 (see map). A free parking garage can be found on Campus and accessed via Eißendorfer Straße 40
Arrival by Airplane
From the airport you can take the public transportation: Local train S1 till Central station/Hauptbahnhof. From there take local train S3 as described in "Arrival by public transport".
You can find the website of the airport here: http://ham.aero/en/