Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing.

This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.

In this second edition, corrections and improvements have been made. In addition, study review questions have been added to each chapter, providing readers with a tool for self-assessment.

Christian Clason is Professor of Mathematical Optimization at the Department of Mathematics and Scientific Computing of the University Graz.