ABSTRACT
The operator theory is the study of linear operators on functional spaces, beginning with differential and integral operators. The operator theory, which depends heavily on the topology of the functional spaces, is a branch of the functional analysis. This chapter reviews the basic notions of the theory of linear operators and functionals, with the aim of discussing properties of the adjoint operators and adjoint boundary value problems. Concept of an operator is a particular case of the general concept of the mapping of one set into another. The spaces of continuous and differentiable functions are more natural for the differential equations. The concept of the operator's closure is closely related with the concept of a strong solution of a problem for a differential equation.
