2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67202This talk is organized as follows: First we explain some basic concepts in non-commutative probability theory in the frame of operator algebras. In Section 2, we discuss related topics in von Neumann algebras. Sections 3 and 4 contain some of the key ideas and results in free probability theory. Last section states some of the important applications of free probability theory.Operator Algebras20C30, 20J05text