BAFA
Tasks and purpose of the Federal Office of Economics and Export Control
The Federal Office of Economics and Export Control (BAFA) is, as the name implies, primarily responsible for the export verification of goods requiring a license. This includes e.g. dangerous chemicals, weapons, radioactive materials, technical equipment for espionage and much more.
On the BAFA website, there are extensive lists that list the entire spectrum of goods that require approval. The processing time of an application can take several weeks to months, which is why an application should be submitted early enough. Further information can be found on Wikipedia.