Coxeter's friezes: algebra, geometry, combinatorics

The notion of frieze pattern was introduced by Coxeter in 1971 and remained almost unknown for many years. Examples of frieze patterns have algeady been considered by Gauss, they are also related to Farey graph and continued fractions. Recently Coxeter's friezes attracted much interest due to their relation to cluster algebras. I will try to give a simple introduction to the subject, explain old and new results and formulate some open problems.