- 1978 Founding of the Group of Functional Analysis by James Bell Cooper.
- 1997 Incorporating of the group as the Department of Functional Analysis into the Institute of Analysis and Numerics.
- 1998 The Department of Dynamic Systems and Approximation Theory as a part of the Institute of Analysis and Numeris is established by Franz Peherstorfer (1950-2009).
- 2001 Founding of the Institute of Analysis with the Department of Functional Analysis and the Department of Dynamic Systems and Approximation Theory. James Bell Cooper headed the institute until his retirement in September 2012.
- 2010 Peter Yuditskii becomes Head of the Department of Dynamic Systems and Approximation Theory. He headed the department until 2021.
- 2012 The Group Nonlinear Resonance Analysis is established by Elena Tobisch.
- October 2012 Michael Schmuckenschläger becomes Head of the Institute of Analysis and Head of the Department of Functional Analysis. He headed the institute and the department until August 2014.
- September 2014 Aicke Hinrichs is appointed to the Johannes Kepler University and becomes Head of the Institute of Analysis and Head of the Department of Functional Analysis. He headed the institute and the department until January 2023.
- September 2023 Paul F.X. Müller becomes Head of the Institute of Analysis and Head of the Department of Functional Analysis.
- September 2023 Elena Tobisch becomes Head of the Department of Dynamic Systems and Approximation Theory. She headed the department until her retirement in February 2024.