The present book is based on lectures that the author has given at the University of Tokyo over the past ten years. It is intended as a textbook that can be studied independently by students or used in a course on functional analysis, i.e., the general theory of linear operators in functional analysis as well as the essential features of their application in various areas of modern and classical analysis. Necessary prerequisites for reading this book are summarized in Chapter 0 under the titles: set theory, topological spaces, measure spaces, and linear spaces, with or without proof. Following this, starting from the chapter on semi-norms, a general theory of Banach and Hilbert spaces is presented in connection with the theory of generalized functions by S. L. Sobolev and L. Schwartz. Although the book is primarily aimed at doctoral students, it is hoped that it may also be useful for research mathematicians.