This book provides a compact presentation of theory, particularly in analysis and linear algebra, which first-year students in natural or engineering sciences should master or refresh as part of a preparatory or bridging course. On the other hand, the book offers numerous exercises closely related to the presented theory, complete with fully worked-out solutions, allowing students to practice and develop their familiarity with the concepts. It is aimed at prospective students who can use it to independently review their school knowledge or as a supplement to a preparatory or bridging course. Following this preparatory course in mathematics, there are two additional books, "Higher Mathematics Compact" and "Workbook for Higher Mathematics," which cover the topics of a one- or two-semester foundational lecture.