Shigeru Mukai (向井 茂, Mukai Shigeru, born 1953) is a Japanese mathematician at Kyoto University specializing in algebraic geometry.

He introduced the Fourier–Mukai transform in 1981 in a paper on abelian varieties, which also made up his doctoral thesis. His research since has included work on vector bundles on K3 surfaces, three-dimensional Fano varieties, moduli theory, and non-commutative Brill-Noether theory. He also found a new counterexample to Hilbert's 14th problem (the first counterexample was found by Nagata in 1959).

• Mukai, Shigeru; Oxbury, W. M. (8 September 2003) [First published 1998], An Introduction to Invariants and Moduli, Cambridge Studies in Advanced Mathematics, vol. 81, Cambridge University Press, ISBN 978-0-521-80906-1, MR 2004218
• Mukai, Shigeru (5 December 2008), モジュライ理論（1） [Moduli Theory (1)], Iwanami Shoten, ISBN 978-400006057-8
• Mukai, Shigeru (5 December 2008), モジュライ理論（2） [Moduli Theory (2)], Iwanami Shoten, ISBN 978-400006058-5
• Mukai, Shigeru (1981). "Duality between ${\displaystyle D(X)}$ and ${\displaystyle D({\hat {X}})}$ with its application to Picard sheaves". Nagoya Mathematical Journal. 81: 153–175. doi:10.1017/S002776300001922X. ISSN 0027-7630.