  This paper presents a complete analysis of the effects of second order
gravitational perturbations on Cosmic Microwave Background anisotropies, taking
explicitly into account scalar, vector and tensor modes. We also consider the
second order perturbations of the metric itself obtaining them, for a universe
dominated by a collision-less fluid, in the Poisson gauge, by transforming the
known results in the synchronous gauge. We discuss the resulting second order
anisotropies in the Poisson gauge, and analyse the possible relevance of the
different terms. We expect that, in the simplest scenarios for structure
formation, the main effect comes from the gravitational lensing by scalar
perturbations, that is known to give a few percent contribution to the
anisotropies at small angular scales.
