Operator algebras are mathematical structures that study linear operators on Hilbert spaces, which are fundamental in quantum mechanics and functional analysis. They provide a framework for understanding the properties and relationships of these operators, often focusing on their algebraic and topological aspects. These algebras can be classified into various types, such as C*-algebras and von Neumann algebras, each with unique properties and applications. Operator algebras play a crucial role in modern mathematics and physics, particularly in the study of quantum systems and the foundations of functional analysis.