2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148320We give an elementary explicit construction of cell decomposition of the moduli space of projective structures on a two dimensional surface analogous to the decomposition of Penner/Strebel for moduli space of complex structures. The relations between projective structures and $PGL(2,{\bf C})$ flat connections are also described. (in the revised version uuencoded pictures are made printable)17 pages, 11 pictures (included)High Energy Physics - TheoryQuantum Algebratext