This second, revised and expanded edition of the textbook previously published under the title "Elementary Geometry and Algebra" more clearly emphasizes the intended integration of mathematics in schools and universities. The new first chapter presents the philosophy of the book along with its central didactic principles. In each of the following five chapters, the first section thoroughly discusses the interaction of the respective topic with school mathematics education. The subsequent mathematical content of the chapters is essentially a revision of the chapters from the first edition. This book assumes a certain level of mathematical education, such as that acquired in the first two semesters of mathematical studies. The chapters can be read independently of one another, and historical contexts have been incorporated wherever possible.