Staying in Germany
About 120 universities in Germany offer the possibiltiy to complete a doctorate after graduation. About 25,000 students earn their doctorate each year. They are of the opinion that it is worth crowning off their studies with a doctor's cap and gown. Detailed information is available at the German Academic Exchange Service, DAAD. You should also inform yourself about the terms of residence for students doing their doctorate.
Post-Graduate Studies are also a possiblity and are realized in much the same way as a Master's. Usually, after a successful completion of undergraduate studies, a (at longest) two-year post-graduate study period can be allowed (as long as the studies up until that point have been completed efficiently).
Because of residence regulations, the choice to study for a second degree after a completed degree is one of the most difficult options for further studies in Germany. If you should aspire to a second degree, you should inform yourself directly at the Kreisverwaltungsreferat (the local authorities) about the possibilities.
You can find further information about study possibilities in Germany in the DAAD Hochschulführer (University Guide).
After successfully completing your degree at a German university your entrance into the work world - which depends on the job market - is a possibility. The residence permit can be extended for up to a year for one who wishes to seek a career suited to their degree. You must have proof of successful completion of your degree, finances, and proper medical insurance. More information is available here.