Lecture Notes on K-Theory and Operator Algebras

Based on lecture courses delivered at the 2025 CIMPA School K-theory and Operator Algebras in Argentina, this volume collects introductory surveys by experts on several active areas of modern K-theory and operator algebras. It explores the rich interconnections among these subjects and their applications to topology, symbolic dynamics, quantum information theory, and noncommutative geometry. Topics include bivariant algebraic and topological K-theory from a higher-categorical perspective, bornological and condensed approaches to functional analysis, self-similar actions and their associated algebras, quantum symmetries and quantum information, subshifts over infinite alphabets, the classifiability of C${}^{\ast }$-algebraic crossed products, and C${}^{\ast }$-algebras associated with twisted groupoids.