general mechanisms electric-magnetic duality, Montonen-Olive duality, geometric Langlands duality string-fivebrane duality string-QFT duality QFT-QFT duality: effective QFT incarnations of open/closed string duality, relating (super-)gravity to (super-)Yang-Mills theory: Seiberg duality (swapping NS5-branes) Classical groups Finite groups Group schemes Topological groups Lie groups Super-Lie groups Higher groups Cohomology and Extensions Related concepts U-duality is a kind of duality in string.