Wussing graduated from high school, and from 1947 to 52 studied mathematics and physics at the University of Leipzig. Ernst Hölder was one of his teachers. In 1952 he took the state examination, and received his doctorate in 1957. His dissertation was on embedding finite groups. From 1956 to 1966 he was assistant at the Karl-Sudhoff Institute for the History of Medicine and Science at the University of Leipzig. He qualified as a professor there in 1966 with a ground-breaking work on the genesis of the abstract group concept. From 1966 to 1968 was Wußing lecturer, and from 1968 professor of history of mathematics and natural sciences. In 1969 his book Genesis of the Abstract Group Concept was published in German; it was translated by Abe Shenitzer and Hardy Grant in 1984. B.H. Newman wrote in Mathematical Reviews (see external link below) that Wussing's "main thesis, ably defended and well documented, is that the roots of the abstract notion of a group do not lie, as frequently assumed, only in the theory of algebraic equations, but they are also to be found in the geometry and in the theory of numbers at the end of the 18th and the first half of the 19th centuries". Newman comments that Wussings bibliography is "oddly arranged". Newman also notes that a broader perspective on the topic would require reading the works of George Abram Miller.
Promoted from a department head at the Karl-Sudhoff Institute, he headed the institute from 1977 to 1982. In 1971 he became a corresponding member of the International Academy of the History of Science, and a regular member in 1981. In 1984 he became a full member of the Saxon Academy of Sciences in Leipzig. Wussing retired in 1992.
Wussing is the author of numerous scientific historical publications, the author of many mathematicians' biographies, and co-editor of several series of publications, including biographies in the Teubner Verlag, and several volumes in the series Klassiker der Exakten Wissenschaften (Ostwald's Classics of the Exact Sciences), in particular on Euler's work on functional theory, Gauss' diary, and Felix Klein's Erlangen program. In 1993 he was awarded the Kenneth O. May Prize. Until 1998 he was Chairman of the Commission for the History of Science at the Saxon Academy of Sciences. He was also involved in the publication of Johann Christian Poggendorff's Biographical and Literary Pocket Dictionary of the History of Exact Sciences.
- Carl Friedrich Gauss. Biography and document, Leipzig, Leipzig Edition on Gutenbergplatz 2011 (Eagle 051)  (The 60-page appendix CF Gauss and BG Teubner in Leipzig for the 200th anniversary of its founding on February 21, BG Teubner, 1811 in Leipzig.)
- Eagle Guide From Leonardo da Vinci and Galileo Galilei. Mathematics and Renaissance, Leipzig, Leipzig Edition on Gutenbergplatz 2010 (Eagle 041) 
- Eagle Guide From Gauss to Poincaré – Mathematics and Industrial Revolution, of Leipzig, Leipzig Edition on Gutenbergplatz 2009 (Eagle 037) 
- Mathematics 6000 years – a cultural and historical journey through time, 2 vols, Berlin / Heidelberg, Springer, 2008, 2009 (range: from scoring marker to the computer )
- (with H. W.Alten, A. Djafari Naini, Folkerts, H. Schlosser, K.-H. Chimneys): 4000 years Algebra, Springer Verlag 2003
- The major renovation – on the history of the scientific revolution, Basel / Boston / Berlin, Birkhäuser 2002
- Publisher: Glossary ABC researcher and inventor, Frankfurt, German Harri 1992
- Editor and co-written biographies of important mathematicians – a collection of biographies, 1975, 4 Edition, Berlin, people and knowledge in 1989
- Editor: History of Science, Cologne, Aulis Verlag 1987
- The Genesis of the abstract group concept, MIT Press 1984 (English translation of the habilitation "The genesis of the abstract group concept – a contribution to the genesis of abstract group theory", 1966)
- Lectures on the History of Mathematics, Berlin, German Academic Publishers 1979
- Mathematics in the period of slave society, Leipzig, Teubner, 1962, and Aachen, Mayer, 1962
- Nicholas Copernicus, Leipzig, 1973 Urania
- Carl Friedrich Gauss, Leipzig, Teubner, 1974, second Edition 1976
- Isaac Newton, Leipzig, Teubner, 1977, 4th Edition 1990
- Adam Ries, Leipzig, Teubner, 1989, 1992, 3rd, revised and expanded edition, Leipzig, Leipzig Edition on Gutenbergplatz 2009 (Eagle 033)
- Kaunzner with Wolfgang, Editor: Coss, Adam Ries, Stuttgart / Leipzig, *Teubner, 1992, facsimile and commentary volumes in a slipcase (Teubner Archive for Mathematics, Supplement 3)
- Menso Folkerts (2007) "Hans Wussing", Journal of History and Ethics of Natural Sciences, Technology, and Medicine 15(4):295–7.
- Entry in the Mathematics Genealogy Project
- B.H. Newman (1969) Review of Genesis of the Abstract Group Concept in Mathematical Reviews.