In Germany, international students who have completed their studies have several options for obtaining a work permit, permanent residency/settlement, and eventually citizenship. Here are some common paths:

1. Job Seeker Visa: After completing your studies in Germany, you may be eligible for a Job Seeker Visa. This visa allows you to stay in Germany for up to six months to search for employment related to your field of study. Once you find a job, you can transition to a work permit.

2. Employment Visa: If you find a job offer in Germany after completing your studies, your prospective employer can sponsor your work permit. The employer needs to prove that there are no suitable candidates from within the European Union (EU) or the European Economic Area (EEA) for the position. The job offer should also meet certain wage and employment conditions. The work permit allows you to work and reside in Germany.

3. Blue Card: If you have a higher education degree and a job offer in Germany that meets certain criteria (such as minimum salary requirements), you may be eligible for the EU Blue Card. This card is designed for highly skilled professionals and allows them to work and reside in Germany. It also offers a path to long-term residency and eventual citizenship.

4. Settlement Permit: After working in Germany for a certain period on a work permit, you may be eligible to apply for a Settlement Permit (Niederlassungserlaubnis). This permit grants you long-term residency and allows you to work and live in Germany without any time restrictions.

5. Family Reunification: If you have a spouse or partner who is a German citizen or holds a permanent residence permit in Germany, you may be eligible to apply for a residence permit based on family reunification. This option allows you to join your family member in Germany and potentially obtain a work permit.

6. German Citizenship: Obtaining German citizenship generally requires residing in Germany for a certain period (usually eight years, reduced to seven years under certain circumstances), meeting language proficiency and integration requirements, renouncing your previous citizenship (unless you are eligible for dual citizenship), and fulfilling other criteria set by the German government.

Please note that immigration rules and policies can change over time, so it's crucial to consult the official website of the German authorities, such as the Federal Office for Migration and Refugees (BAMF) or the German Missions abroad, for the most up-to-date information and requirements related to work permits, residency, and citizenship.