The book provides a comprehensive insight into central aspects of the subject areas of Analytical Geometry and Linear Algebra in upper secondary education (S II). It serves as a guide for students pursuing a teaching degree at the high school level, as well as for teachers who wish to make the instruction in this often perceived as dry subject area more lively and engaging. The book takes into account the new educational standards for S II and consistently follows key didactic principles: developing a solid foundational understanding of central concepts and relationships while highlighting fundamental ideas, ensuring clarity while carefully making abstractions, connecting to the curriculum content of lower secondary education (S I), and establishing links to other areas of mathematics taught in S II, as well as addressing interesting and appealing applications for students.