This book offers practical assistance and subject-specific advice for first-year mathematics students and their areas of application. It addresses the peculiarities of higher mathematics as well as the associated work and thought processes, while also tackling more general challenges of studying: it explains not only central concepts and approaches in mathematics but also the effective use of available time and how to deal with abstract intellectual challenges. A variety of tips make it easier to competently handle the shift in focus from calculation to proof, maintain an overview during studies, learn independently and sustainably, and keep the enthusiasm for the subject alive. This creates optimal conditions for a successful engagement with mathematics.