  In this paper we study Newton's method for solving the generalized equation
$F(x)+T(x)\ni 0$ in Hilbert spaces, where $F$ is a Fr\'echet differentiable
function and $T$ is set-valued and maximal monotone. We show that this method
is local quadratically convergent to a solution. Using the idea of majorant
condition on the nonlinear function which is associated to the generalized
equation, the convergence of the method, the optimal convergence radius and
results on the convergence rate are established. The advantage of working with
a majorant condition rests in the fact that it allow to unify several
convergence results pertaining to Newton's method.
