With a population of over 20 million, Shanghai is a busy and highly mobile city. Public transport is convenient and highly developed. The cheapest way to get around Shanghai for shorter distances is by bike. You may buy yourself a new or second-hand bike for 50 Euro, but you are more likely to ride the brightly colored bikes of one of the many bike-sharing services now available in Shanghai (and all major cities). They are very cheap, available on every street corner and can be booked and unlocked with an app on your mobile phone.
Commuting by metro is fast, easy and cheap: 50 Euro cents per ride. The Shanghai Metro currently runs 14 lines. There are 2 metro stops near Fudan University and Tohee, called Jiangwan Stadium Station and Guoquan Road station, both on Metro Line 10, which will bring you directly to most places of interest in the city center as well as to Hongqiao Airport.
But most of the time, you will find yourself catching a taxi if you head to town. Taxis are very affordable, a ride from your dorm to the city center will set you back 4 to 5 Euro. Didi is the local Uber and probably one of the first apps that you will download on your phone once in Shanghai.