2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/34153Basic notions and mathematical tools in continuum media mechanics are recalled. The notion of exponent of a covariant differential operator is introduced and on its basis the geometrical interpretation of the curvature and the torsion in $(\bar{L}_n,g)$-spaces is considered. The Hodge (star) operator is generalized for $(\bar{L}_n,g)$-spaces. The kinematic characteristics of a flow are outline in brief. PACS numbers: 11.10.-z; 11.10.Ef; 7.10.+g; 47.75.+f; 47.90.+a; 83.10.Bb34 pages, LaTeXGeneral Relativity and Quantum CosmologyMechanics of Continuous Media in $(\bar{L}_n,g)$-spaces. I. Introduction and mathematical toolstext