This book is primarily aimed at students who are attending introductory courses in university mathematics as part of a natural sciences or engineering degree, and it is intended as a targeted preparation for the start of their studies. Drawing on the author's close connection to the subject and years of experience in leading tutorial groups, it successfully combines clear explanations with the necessary academic precision. Through numerous examples and a clear structure, the book refreshes knowledge from high school and middle school, provides initial insights into university mathematics in the areas of analysis and linear algebra, and simultaneously offers an overview of the structure of common mathematics courses. It serves as an ideal preparation for the beginning of studies and is also useful as a reference work in the first semesters.