2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196873This paper provides a review of some recent issues on the Mixmaster dynamics concerning the features of its stochasticity. After a description of the geometrical structure characterizing the homogeneous cosmological models in the Bianchi classification and the Belinsky-Khalatnikov-Lifshitz piecewise representation of the types VIII and IX oscillatory regime, we face the question regarding the time covariance of the resulting chaos as viewed in terms of continuous Misner-Chitré like variables. Finally we show how in the statistical mechanics framework the Mixmaster chaos raises as semiclassical limit of the quantum dynamics in the Planckian era.20 pages, wide review and new resultsGeneral Relativity and Quantum Cosmologytext