  Equations of associativity in two-dimensional topological field theory (they
are known also as the Witten-Dijkgraaf-H.Verlinde-E.Verlinde (WDVV) system) are
represented as an example of the general theory of integrable Hamiltonian
nondiagonalizable (i.e., do not possessing Riemann invariants) systems of
hydrodynamic type. A corresponding local nondegenerate Hamiltonian structure of
hydrodynamic type (Poisson bracket of Dubrovin-Novikov type) is found. For n=3
the equations of associativity are reduced to the integrable three wave system
by a chain of explicit transformations. Any solution of the integrable three
wave system generates solutions of the equations of associativity. Explicit
B\"acklund type transformations connecting solutions of different equations of
associativity are found.
