  We consider the problem of global in time existence and uniqueness of
solutions of the 3-D infinite depth full water wave problem. We show that the
nature of the nonlinearity of the water wave equation is essentially of cubic
and higher orders. For any initial interface that is sufficiently small in its
steepness and velocity, we show that there exists a unique smooth solution of
the full water wave problem for all time, and the solution decays at the rate
$1/t$.
