NONEXTENSIVE STATISTICAL MECHANICS AND THERMODYNAMICS -- INTRODUCTION, FOUNDATIONS AND APPLICATIONS Prof. Constantino Tsallis Head of the Condensed Matter and Statistical Physics Department Brazilian Center For Physics Research, Rio de Janeiro - Brazil Visiting: Jan 23-26, 2005. Seminar Jan 24, 2005. ABSTRACT: The cornerstones of Boltzmann-Gibbs and nonextensive statistical mechanics respectively are the usual entropy and a specific generalized form. Through them we revisit the concept of additivity and other basic thermostatistical notions. These current questions will be addressed as an introduction to nonextensive statistical mechanics. Its dynamical foundations and some of its various recent applications (in physics, geophysics, chemistry, economics, biology, information theory, linguistics, time series, image processing, cognitive psychology, among others) will be briefly reviewed as well. Bibliography: M. Gell-Mann and C. Tsallis, eds., "Nonextensive Entropy - Interdisciplinary Applications" (Oxford University Press, New York, 2004), and http://tsallis.cat.cbpf.br/biblio.htm