This quantity comprises the lawsuits of the foreign Workshop on Tropical and Idempotent arithmetic, held on the autonomous collage of Moscow, Russia, from August 26-31, 2012. the most goal of the convention used to be to assemble and unite researchers and experts in a variety of parts of tropical and idempotent arithmetic and functions. This quantity includes articles on algebraic foundations of tropical arithmetic in addition to articles on functions of tropical arithmetic in numerous fields as varied as economics, electroenergetic networks, chemical reactions, illustration concept, and foundations of classical thermodynamics. This quantity is meant for graduate scholars and researchers drawn to tropical and idempotent arithmetic or of their functions in different parts of arithmetic and in technical sciences.