This book presents an overview of the essential elements of functional analysis and its branches that are closely related to the challenges of computational mathematics and its applications. It covers key aspects of the theory of variational equations, generalized solutions, and Sobolev spaces, as well as extreme problems in approximation theory, numerical integration theory, variational methods, composition methods, and iterative techniques, including Chebyshev methods. Additionally, it discusses explicit stable difference schemes for solving stiff systems of equations. Aimed at undergraduate and graduate students specializing in computational or applied mathematics, as well as educators and engineers interested in the applications of functional analysis, this book serves as a valuable resource for those looking to deepen their understanding of the subject.