Abstract
<jats:p>The purpose of this book is to present the theory and methods of functional analysis that are applied to the study of differential equations in various function spaces, including spaces of generalized functions - such as Sobolev spaces - as well as normed and Hilbert spaces. The first part of the book focuses on examining the topological structures of the spaces of basic functions and justifying the definitions of convergence in these spaces; the second part addresses properties of bounded and unbounded operators in normed spaces, including properties of closedness, symmetry, and self-adjointness. Furthermore, the spectra of many operators - both bounded and unbounded - are constructed, including the spectrum of the Sturm-Liouville operator. Each section of the book provides numerous examples and solved problems, which help the reader master practical applications of the methods of functional analysis described. The textbook is intended for advanced undergraduate students, as well as master's and doctoral students. The material of the book is based on lectures and seminar sessions conducted by the authors at the Faculty of Computational Mathematics and Cybernetics, Moscow State University.</jats:p>