Table of Contents

• Preface
• Early triumphs
• Approximation
• Operator theory
• Harmonic analysis
• Banach algebras: The Gleason-Kahane-Żelazko theorem
• Complex dynamics: The Fatou-Julia-Baker theorem
• The prime number theorem
• Coda: Transonic airfoils and SLE
• Liouville’s theorem in Banach spaces
• The Borel-Carathéodory inequality
• Phragmén-Lindelöf theorems
• Normal families