Catalan numbers and root systems S.Fomin The Catalan numbers and their generalizations and refinements can be viewed as "type A" versions of more general numbers defined for an arbitrary finite Coxeter group. These numbers come up in a variety of combinatorial, algebraic, and geometric contexts to be surveyed in the talk (hyperplane arrangements, noncrossing partitions, generalized associahedra, and so on), suggesting connections that transcend mere numerology. Joint work with N.Reading.