Operator Algebra is a branch of mathematics that studies operators, which are functions that act on elements of a space, often in the context of Hilbert spaces or Banach spaces. It focuses on the algebraic properties of these operators, such as addition, multiplication, and composition, and how they can be represented and manipulated. In quantum mechanics, operator algebra plays a crucial role, as physical observables like position and momentum are represented by operators. This framework allows for the formulation of quantum theories and the analysis of their properties, providing a mathematical foundation for understanding complex systems in physics.