Linear Functional Analysis: An Application-Oriented Introduction in Bloomington, MN

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it 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 Analysis
will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.