In 18th century France and Germany, new textbooks for teaching the mathematical sciences in higher education, which were usually entitled “Cours de Mathmatique(s)” and “Mathematische Anfangsgrnde”, appeared. They are scientific introductory textbooks, which were mainly created to assist the teaching of the mathematical sciences at universities and to be used by the students. They contain a variety of subjects associated with the wide-ranged label of mathematical sciences at that time. This included not only pure, but also the so-called applied mathematics, like mechanics, statics, and optics.Remarkably, these textbooks were written in the national languages – French and German. The work by Confalonieri/Krger provides firstly an overview of the French and German educational systems in the 18th century; then, an analysis of a selection of some of the most used French and German textbooks for teaching the mathematical sciences, their contents, and their pedagogical approaches follows. The main aim is to point out the similarities and differences between the considered textbooks and, as much as possible, between the corresponding educational systems.