Troitsk: Troitsk branch of the state educational institution of higher professional education "Chelyabinsk State University", 2012. 206 s. 2nd Edition . , spr. and dop. This tutorial is the final, fifth part of the course Functional analysis and is devoted to the consideration of the theory of inverse operators, completely continuous operators, as well as the spectral theory of operators. The Theory of Integral Equations . The structure of the allowance is no different from the previous parts, and is their natural continuation. The manual presents theoretical and practical material on the topics "Inverse operators", "quite continuous operators", "Spectral theory of self-adjoint and quite continuous operators" .. The manual is distinguished by a summary brevity and simplicity of presentation . The solution of the most complex problems is given as examples, to many problems for independent solution are given instructions. The training manual is intended for teachers and students. Can be used to conduct practical classes and organize independent work of students.