The thermodynamic of Lie groups has been introduced by Jean-Marie Souriau during the 20th century. It aims at rewriting the notions of statistical and thermodynamic equilibrium in terms of invariance under the action of groups of symmetries, and allows to formulate statistical mechanics in a symplectic framework. The topic has gained attention recently due to some established links with information geometry , Lie theory and symmetric spaces geometry. In this talk, we will present the main objects and structures arising from this theory and give a brief insight of its usefulness in other domains.