The majority of the German population is subject to compulsory insurance. In most insurance schemes, both employer and employee pay equal contributions into the social security system. In addition, there are non-mandatory insurances, such as liability insurance.
An overview of all insurances in Germany can be found here.

Health Insurance

Health insurance is mandatory in Germany for researchers and accompanying family members (more information in 40 languages). You need the health insurance certificate for the issuance of a residence permit and the conclusion of an employment contract.
The insurance must at least cover medical treatment in case of acute illness and accidents.

More information.

Pension Insurance

The statutory pension insurance in Germany is one of the core elements of the German welfare state.
All persons working in Germany, regardless of their nationality, are obliged to pay contributions to the German pension insurance.
Exceptions include scholarship holders, civil servants and employees who receive their salary from employers based outside Germany.

More information.

Liability insurance

If you or your children cause any sort of damage in a private context or harm somebody, you are normally held responsible for all costs. In that case it is irrelevant whether is was on purpose or a misfortune. In order to avoid that, it is highly recommended to have a liability insurance. This insurance is no mandatory insurance.
Possible German insurance companies are HanseMerkur, BavariaDirekt, LVM Versicherungen and Gothaer. If you are looking for an insurance that offers English speaking service, you might also want to have a look at Vela.
Additionally, you can compare various offers and choose the one that fits best for you on Check24.