Mandatory and above all legally required is a health insurance. You can find more information here. Furthermore, every enrolled student is insured against accidents during certain activities by the Unfallkasse Nord. Information on accident insurance is available here.
A mishap can happen quickly. And if it happens on an apparatus in a TUHH laboratory, it can quickly become expensive. The Studierendenwerk Hamburg has prepared information on the topic of liability insurance in the download area of its website. We recommend you take a look.