1 Fundamentals
1.1 What is Functional Analysis?
1.2 Normed Linear Spaces
1.3 Finite-Dimensional Spaces
1.4 Linear Operators
1.5 The Baire Category Theorem
1.6 The Three Big Results
1.7 Applications of the Big Three
2 Ode to the Dual Space
2.1 Introduction
2.2 Consequences of the Hahn-Banach Theorem
3 Hilbert Space
3.1 Introduction
3.2 The Geometry of Hilbert Space
4 The Algebra of Operators
4.1 Preliminaries
4.2 The Algebra of Bounded Linear Operators
4.3 Compact Operators
5 Banach Algebra Basics
5.1 Introduction to Banach Algebras
5.2 The Structure of a Banach Algebra
5.3 Ideals
5.4 The Wiener Tauberian Theorem