  We study word series and extended word series, classes of formal series for
the analysis of some dynamical systems and their discretizations. These series
are similar to but more compact than B-series. They may be composed among
themselves by means of a simple rule. While word series have appeared before in
the literature, extended word series are introduced in this paper. We exemplify
the use of extended word series by studying the reduction to normal form and
averaging of some perturbed integrable problems. We also provide a detailed
analysis of the behaviour of splitting numerical methods for those problems.
