This book is an attempt to emulate the classroom learning experience. It seems appropriate in a world where online education has become par for the course and the student does not always have access to a teacher who can help fill in the blanks. As a result, the book is thorough (sometimes to a fault) and somewhat more conversational than most others of its ilk.

The classroom is a place where one often engages in free-wheeling discussions that cut across disciplines. The subject of Functional Analysis, which lies at the confluence of modern analysis, algebra and topology, seems well-placed to transfer such discussions to the written word. It seamlessly mixes ideas from these different subjects, is widely applicable, and is therefore appealing to a broad spectrum of people. My hope is to present an introduction to the subject that is useful to everyone, regardless of their tastes.

The book is intended to be used for a year-long course in Functional Analysis aimed at Master's or Ph.D. students. After a short review in Chapter 1, Chapters 2–6 constitute the core of the subject. Here, one proves the Hahn-Banach theorems, the consequences of the Baire Category theorem, and the Banach-Alaoglu and Krein-Milman Theorems. Barring a few specialized topics, these chapters may be taught in a single semester.

The second half of the book (Chapter 7–10) is a little more advanced, and is meant to be taught in the second semester as an introduction to the theory of Operator Algebras. Ostensibly, the goal is to prove the Spectral Theorem for Normal Operators on a Hilbert space. However, I have chosen to take the scenic route, introducing as much operator algebra theory as I can given the time constraints. Perhaps the most egregious detour is in Chapter 9, where one encounters a proof of the Riesz-Markov-Kakutani theorem (due to Garling) that uses C*-algebra theory. I hope that such discussions will encourage students to look further into this fascinating subject.

A word on the exercises: there are plenty of them at the end of each chapter. Many are there to complement the results proved in the text, while others are there to allow students to practice using these results.