  This paper continues the study of cluster algebras initiated in
math.RT/0104151. Its main result is the complete classification of the cluster
algebras of finite type, i.e., those with finitely many clusters. This
classification turns out to be identical to the Cartan-Killing classification
of semisimple Lie algebras and finite root systems, which is intriguing since
in most cases, the symmetry exhibited by the Cartan-Killing type of a cluster
algebra is not at all apparent from its geometric origin.
  The combinatorial structure behind a cluster algebra of finite type is
captured by its cluster complex. We identify this complex as the normal fan of
a generalized associahedron introduced and studied in hep-th/0111053 and
math.CO/0202004. Another essential combinatorial ingredient of our arguments is
a new characterization of the Dynkin diagrams.
