The plane geometry by Koecher and Krieg emphasizes, unlike comparable textbooks in this field, the analytical perspective. In addition to an introduction to the axiomatic geometry of affine and projective planes, classical school geometry is addressed using methods from linear algebra. Advanced results include, for example, Feuerbach's theorem, Morley's theorem regarding the triangle formed by the angle bisectors, and Pascal's theorem about curves of the second degree. The book offers a well-structured teaching text on geometry, particularly suitable for education students, teachers, and mathematics educators, but also for high school students. The new edition includes Connes' theorem from 1999 with a new proof of Morley's theorem, as well as an additional section on the complex double ratio a.