This book is designed to help students in their first semesters transition from school mathematics to university mathematics. It is therefore an excellent resource for supporting and complementing bridge courses offered by many universities before the start of studies. The author provides a comprehensive overview of the areas of analysis, differential geometry, and linear algebra, preparing readers to work with derivatives, complex numbers, matrices, vectors, and tensors. The most common hurdle for first-year students is the deductive approach of lectures, where it seems that definitions "fall from the sky." The author overcomes this problem by forming mathematical concepts based on background information that promotes understanding. Additionally, numerous worked examples and illustrations, as well as connections to prior knowledge, are taken into account.