This paper attempts to relate some ideas of Grothendieck in his Esquisse d'un programme and some of the recent results on 2-dimensional topology and geometry. Especially, we shall discuss the Teichmller theory, the mapping class groups, $ SL (2,\bold C) $ representation variety of surface groups, and Thurston's theory of measured laminations.

We discuss some applications of an intrinsic multipication in the space of simple loops in a surface.