Linear functional analysis is a largely canonical subfield of mathematics that is aesthetically appealing in its synthesis of algebra, topology, and analysis. This book provides a concise, well-structured, and well-written introduction to this area, also offering the necessary knowledge from measure theory. It is particularly suitable for readers who want to quickly grasp the central statements. The book contains complete proofs of all mathematical theorems and numerous exercises, most of which come with solutions. The sixth edition, now available, has been revised once more, establishing it as a standard work in the field of functional analysis, especially aimed at readers interested in applications to differential equations.