This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theoryit explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory.
A complete introduction to the subject,Linear Functional Analysiswill be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.