For your enrolling at the University of Hamburg, please have a look at the informations at our International Office. It is very important, that you follow the detailed instructions (PDF) for your online application.
The enrolment is only possible for a full term (summer term: April-September or winter term: October-March) of 6 months. The costs for enrolling at the University of Hamburg are about 350 Euro; this includes a ticket for public transport (bus, trains) for the full period of 6 months. Every student of the University of Hamburg has to pay this ticket, regardless if they are Erasmus students or not.
If you are visiting lectures, you need to do the enrolment. However, if you do an internship in the lab, it is not necessary to do the enrolment. This saves you some money, but on the other hand you don't get a ticket for public transport. Instead you can get monthly student tickets from the public transport association (HVV) if required. If you do an internship in the lab i.e. from January to June, and want to do the enrolment, you have to enrol for 2 terms (winter and summer in this case).
If you want to stay in one of the students houses, accommodation is only available for a full term (summer term: April-September or winter term: October-March) and enrolment is required.