Information on how to apply and a list of partner universities can be found here:
https://www.tu-braunschweig.de/erasmus/vor-dem-aufenthalt
Select "Faculty 3" and then the correct tab:
The application deadline is always 31 January for the following winter and summer semester. After this date, applications for remaining places are possible.
List of exchange programmes of the International Office
You can print out a transcript of records in English (Notenspiegel), which you will need for many applications for a study or internship place abroad, in the QIS / Lecture Portal. If required, it can be stamped by the Examinations Office.