Qualified vocational training
If you want to engage in Germany in employment that requires a qualified vocational training, a limited stay on the basis of the residence title Blue Card EU according to § 19a AufenthG is possible.
If you want to engage in research, you can apply for a stay on the basis of § 20 AufenthG.
Furthermore, in exceptional cases you can also apply for an unlimited residence title, i.e. a settlement permit for highly qualified workers according to § 19 AufenthG.
For these residence titles you usually do not have to prove language skills.