This book provides 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 topics. The text is self-contained and includes all proofs, as well as many exercises, most of which have solutions. Furthermore, there are several appendices, including one on Lebesgue integration theory. A complete introduction to the subject, linear functional analysis will be particularly useful to readers who want to quickly grasp the key concepts and are interested in applications to differential equations.