This volume contains the proceedings of the International Workshop on Tropical and Idempotent Mathematics held at the Independent University of Moscow Russia from August 26-31 2012. The main purpose of the conference was to bring together and unite researchers and specialists in various areas of tropical and idempotent mathematics and applications. This volume contains articles on algebraic foundations of tropical mathematics as well as articles on applications of tropical mathematics in various fields as diverse as economics electroenergetic networks chemical reactions representation theory...