Marcoux L.W. An Introduction to Functional Analysis

4th. ed. — Waterloo (Canada): University of Waterloo, 2018. — 186 p.Preface to the Fourth Edition - December 13, 2018.
Preface to the Third Edition - October 24, 2014.
Preface to the First Edition - December 1, 2008.
Normed Linear Spaces.
An introduction to operators.
Hilbert space.
Topological Vector Spaces.
Seminorms and locally convex spaces.
The Hahn-Banach theorem.
Weak topologies and dual spaces.
Extremal points.
The chapter of named theorems.
Operator Theory.
Appendix – topological background.