• 1978 Founding of the Group of Functional Analysis by James Bell Cooper.
• 1997 Incorporating 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, headed by James Bell Cooper until his retirement in 2012.
• 2010 Peter Yuditskii becomes Head of the Department of Dynamic Systems and Approximation Theory.
• 2012 The Group Nonlinear Resonance Analysis is established by Elena Tobisch.
• September 2014 Aicke Hinrichs was appointed to the Johannes Kepler University. He was Head of the Institute of Analysis and Head of the Department of Functional Analysis until January 2023.

Until 2022 present and former members of the Institute of Analysis have published over 650 articles in mathematical, physical and economics journals, including 6 advanced research monographs. The high quality of publications and research projects demonstrate the coauthorship of leading scientists, including 1 Nobel laureate, 1 Kyoto Prize winner, 4 Fields-Medallists,  2 Fellows of the Royal Society and 6 Salem prize winners.