This report is part of a series whose aim is to present in a synthetic way the major methods of «analytic combinatorics» needed in the average--case analysis of algorithms. It develops a general approach to the distributional analysis of parameters of elementary combinatorial structures like strings, trees, graphs, permutations, and so on. The methods are essentially analytic and relie on multivariate generating functions, singularity analysis, and continuity theorems. The limit laws that are derived mostly belong to the Gaussian, Poisson, or geometric type.