2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64744The determinant is a main organizing tool in commutative linear algebra. In this review we present a theory of the quasideterminants defined for matrices over a division algebra. We believe that the notion of quasideterminants should be one of main organizing tools in noncommutative algebra giving them the same role determinants play in commutative algebra.amstex; final version; to appear in Advances in MathQuantum AlgebraRings and Algebras16W30;15A15;05E05text