Hilbert Spaces

This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH. The text has a strict logical order, in the style of "Definition – Theorem – Proof - Example - Exercises. The proofs are rather thorough and there many examples.The first part of the book(the first three chapters, resp. the first two volumes) is devoted to the theory of Banach spaces in the most general sense of the term. The purpose of the first chapter (resp. first volume) is to introduce