This book is based on lectures at the Technical University of Munich and primarily covers topics that are typically part of the "Analysis" courses in the first two semesters of the Bachelor's program in Mathematics and Physics. These topics include the fundamental building blocks of one-dimensional analysis, such as convergence, continuity, differentiation, and integration, as well as an introduction to differentiability in multiple dimensions, the concept of convergence in metric spaces, and elementary solution methods for ordinary differential equations. The book is distinguished by numerous motivating examples, while still maintaining the necessary mathematical precision. It is excellent both as a reference work and as supplementary reading for the lectures.