This convenient compilation of two volumes into a single edition introduces a wide range of ideas and techniques required for the study of linear differential operators. The first part focuses on the elementary theory of linear differential operators, and the second part on linear differential operators in Hilbert space. All the necessary theorems in functional analysis are developed within the text, making this a self-contained and highly accessible treatment. Written by a world-renowned mathematician, it is appropriate for graduate-level courses. 
Part I keeps the methods of functional analysis in the background while emphasizing the properties of functions of a complex variable. It presents a detailed investigation of the eigenvalue problem for ordinary differential equations with complex coefficients and regular boundary conditions. Part II begins with a compact account of the theory of linear operators in separable Hilbert spaces. Subsequent chapters explore the properties of symmetric operators derived from ordinary differential expressions with real coefficients, as well as the spectral theory of such operators and the corresponding eigenfunction expansions in square-integrable function spaces. Additional topics include the determination of the deficiency indices and the inversion of the Sturm-Liouville problem.