We discuss a two-week summer course on “Network Science” and “Complex Systems” that we taught for 15 German high-school pupils of ages 16–18. In this course, we covered topics in graph theory, applied network science, programming, and dynamic systems alike. We find that “Network Science” is a well-suited course for introducing students to university-level mathematics. We reflect on difficulties regarding programming exercises and the discussion of more advanced topics in dynamic systems. We make the course material available and encourage fellow network scientists to organize similar outreach events.