In many domains the units may be more complex than the standard one due to the fact that they may have internal variation and may bestructured. For example, huge data sets are recorded in O cial Statistics as well as in Companies. Summarizing such information in shorter sets of new + statistical units is a question of increasing importance. In reducing the data set and losing the least information possible, these statistical units yield to more complex data . Their description needs data tables called \symbolicdata tables" because the cells of such data tables may contain not only single numerical or categorical values, but much more complex information, such as: subsets of categorical variable values, intervals of ordinal variable values, histograms, probability distributions, dependencies. Moreover, taxonomies and rules may be given. The need to extend standard data analysis methods (exploratory, clustering, factorial analysis, discrimination,...) to symbolic data table is growing due to the need to get more accurate information and to summarize extensive data sets. We call \Symbolic Data Analysis" (SDA) the extension of standard Data Analysis to such tables. \Symbolic objects" are de ned they describe in an explanatory way classes of units described by symbolicdata. They constitute one of the main output of a SDA. A symbolic object is \complete" if its \extent" covers exactly the class that it describes. The set of complete symbolic objects constitutes a Galois lattice (Diday, Emilion (1996)). We s h o w that this result can be extended to the case of given rules and taxonomies under some natural conditions. Some of the SDA tools developed in the European Community project \SODAS" are mentioned. Some mathematical results clarify links between the symbolic objects provided in the output and the associated Galois lattice of symbolic objects.