2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66452We give an introduction to the theory of determinantal ideals and rings, their Groebner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the Knuth-Robinson-Schensted correspondence. The article contains a section treating the basic results about the passage to initial ideals and algebras.58 pages The newest version has some typos corrected and uses the AMS styleCommutative Algebra05E10, 13F50, 13F55, 13H10, 13P10, 14M12text