A Presentation of the Mapping Class Groups
  Using the works of Gervais, Harer, Hatcher and Thurston and others, we show that the mapping class group of a compact orientable surface has a presentation so that the generators are the set of all Dehn twists and the relations are supported in subsurfaces homeomorphic to the one-holed torus or the four-holed sphere. It turns out that all the relations were discovered by Dehn in 1938. 
Feng Luo