In this chapter we present a further approach toward diophantine analysis. Geometry of numbers was created by Minkowski  at the turn to the twentieth century. In this theory arithmetic results are proved by using geometric arguments; in this sense, geometry rules arithmetic. Originated as a tool in number theory, nowadays geometry of numbers also plays a signiﬁcant role in several other ﬁelds, e.g., cryptography, coding theory, and numerical integration. However, we will only sketch its applications to diophantine analysis.