This book, a translation of the German volume n-Ecke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra in a form that is easily accessible to the student who lacks a sophisticated background in mathematics. It stimulates geometrical thought by applying the tools of linear algebra and the algebra of polynomials to a concrete geometrical situation to reveal some rather surprising insights into the geometry of n-gons. The twelve chapters treat n-gons, classes of n-gons, and mapping of the set of n-gons into itself. Exercises are included throughout, and two appendixes, by Henner Kinder and Eckart Schmidt, provide background material on lattices and cyclotomic polynomials. (Mathematical Expositions No. 18)