What do I have to do if I want to stay in Germany after graduation?

Graduates of German universities can apply for a job seeker visa of 18 months and use this time to find employment in Germany. Please find further information here: https://www.make-it-in-germany.com/en/visa-residence/types/job-search-opportunity-card

Once you receive a job offer, you have to apply for a work visa at the immigrations office.