In mathematics, operator theory is the branch of functional analysis which deals with bounded linear operators and their properties. It can be split crudely into two branches, although there is considerable overlap and interplay between them. These extend the spectral theory, for bounded operators.
Single operator theory
Single operator theory deals with the properties and classification of single operators. For example, the classification of normal operators in terms of their spectra falls into this category.
Operator algebras
The theory of operator algebras brings algebras of operators such as C*-algebras to the fore.