2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35092A review on the main results concerning the algebraic and differential properties of the averaging and coordination operators and the properties of the space-time averages of macroscopic gravity is given. The algebraic and differential properties of the covariant space-time averaging procedure by means of using the parallel transportation averaging bivector operator are analyzed. The structure of the pseudo-Riemannian space-time manifolds of general relativity averaged by means of this procedure is discussed. A comparison of both procedures is given and the directions of further development of space-time averaging procedures of the physical classical fields are outlined.28 pages, LaTeXGeneral Relativity and Quantum Cosmologytext