2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/19372We briefly review the present status of nonextensive statistical mechanics. We focus on (i) the central equations of the formalism, (ii) the most recent applications in physics and other sciences, (iii) the {\it a priori} determination (from microscopic dynamics) of the entropic index $q$ for two important classes of physical systems, namely low-dimensional maps (both dissipative and conservative) and long-range interacting many-body hamiltonian classical systems.Brief review to appear in Annals of the Brazilian Academy of Sciences [http://www.scielo.br/scielo.php] Latex, 7 figsStatistical Mechanicstext