Аннотация:This paper deals with the notion of the Hausdorff dimension in the framework of the thermodynamic formalism. In contrast to previous results, the main contribution of the authors is that they essentially make use of the thermodynamic formalism in the sense of Dobrushin-Lanford-Ruelle, which seems more natural and transparent. This approach allows them to consider more general geometric constructions of fractal sets in metric spaces and constructions determined by symbolic systems on lattices of any dimension. The Hausdorff dimension of the configuration space and of its images with respect to restriction maps is also studied.