  We prove the quasi-optimal convergence of a standard adaptive finite element
method (AFEM) for nonlinear elliptic second-order equations of monotone type.
The adaptive algorithm is based on residual-type a posteriori error estimators
and D\"orfler's strategy is assumed for marking. We first prove a contraction
property for a suitable definition of total error, which is equivalent to the
total error as defined by Casc\'on et al. (in SIAM J. Numer. Anal. 46 (2008),
2524--2550), and implies linear convergence of the algorithm. Secondly, we use
this contraction to derive the optimal cardinality of the AFEM.
